!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_CuZr__MO_407917731909_001 Supported species : Cu Zr 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 = Cu | a0 = 3.6133155822753906 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 2.745433815074483e-01 2.745433815072144e-01 2.33924e-13 3.55060e-12 2 -5.595297462564718e-01 -5.595297462645660e-01 8.09419e-12 2.09082e-10 3 -8.170859919067095e-01 -8.170859919402415e-01 3.35320e-11 1.28172e-10 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -2.230222823547062e+00 -2.230222823554670e+00 7.60769e-12 1.63194e-10 2 2.177954407941684e+00 2.177954407941902e+00 2.17604e-13 2.75993e-10 3 5.775715297678174e-01 5.775715297621007e-01 5.71676e-12 3.10237e-11 ----------------------------------------------------------------------------------------------------- 3 Cu 1 1.194281012991826e+00 1.194281012993866e+00 2.04015e-12 3.14614e-10 2 3.786803345178938e-01 3.786803345160338e-01 1.86001e-12 2.05937e-10 3 -4.266925037434067e-01 -4.266925037385885e-01 4.81815e-12 7.09374e-11 ----------------------------------------------------------------------------------------------------- 4 Cu 1 6.700123108436721e-01 6.700123108429336e-01 7.38520e-13 4.82038e-10 2 1.044210776323923e+00 1.044210776330806e+00 6.88316e-12 9.93006e-11 3 9.550672619664908e-01 9.550672619169782e-01 4.95126e-11 1.48796e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 1.031674927191847e+00 1.031674927194965e+00 3.11773e-12 4.14136e-10 2 -2.212814634630095e+00 -2.212814634625408e+00 4.68781e-12 3.16889e-11 3 5.120031439539092e-01 5.120031439404730e-01 1.34363e-11 1.86757e-10 ----------------------------------------------------------------------------------------------------- 6 Cu 1 1.184310588935253e-01 1.184310588967387e-01 3.21347e-12 5.83710e-11 2 1.095462292675250e+00 1.095462292658111e+00 1.71392e-11 2.19625e-10 3 1.880278468818779e-01 1.880278468495191e-01 3.23588e-11 5.20867e-11 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.151446156046012e+00 1.151446156027211e+00 1.88016e-11 5.47258e-11 2 -3.122530950035265e+00 -3.122530950026895e+00 8.37064e-12 4.30459e-10 3 -3.229736643586214e+00 -3.229736643676437e+00 9.02225e-11 1.91898e-10 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -2.152251655968523e+00 -2.152251655987236e+00 1.87126e-11 4.04702e-10 2 -7.771367607677581e-01 -7.771367607889393e-01 2.11813e-11 1.61871e-09 * 3 -7.346894640205018e-01 -7.346894640987125e-01 7.82107e-11 2.25095e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 -1.278453259158850e-02 -1.278453258656879e-02 5.01970e-12 9.51561e-11 2 -1.202047307213603e+00 -1.202047307247802e+00 3.41993e-11 3.92470e-10 3 -3.636052774766267e-01 -3.636052774751606e-01 1.46605e-12 8.51570e-11 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -1.265061798512808e+00 -1.265061798511822e+00 9.85878e-13 1.01168e-10 2 1.373322481929528e+00 1.373322481947130e+00 1.76015e-11 2.28714e-10 3 -1.513021761195154e+00 -1.513021761160208e+00 3.49460e-11 2.95928e-11 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -3.660992731024319e-01 -3.660992730991632e-01 3.26866e-12 8.18793e-10 2 -1.526232155859477e+00 -1.526232155847383e+00 1.20943e-11 4.29987e-11 3 3.822280769641831e-01 3.822280770044710e-01 4.02878e-11 1.50021e-10 ----------------------------------------------------------------------------------------------------- 12 Cu 1 3.245283374096272e-01 3.245283374001051e-01 9.52211e-12 1.62014e-10 2 7.671033396989407e-01 7.671033396880216e-01 1.09192e-11 3.71183e-11 3 6.709628358859755e-01 6.709628358880376e-01 2.06213e-12 1.47439e-10 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -1.171373790724429e+00 -1.171373790698186e+00 2.62430e-11 3.35050e-11 2 -2.577520257579663e+00 -2.577520257594461e+00 1.47979e-11 1.25847e-09 * 3 -3.321806364402816e+00 -3.321806364421702e+00 1.88853e-11 8.54714e-10 ----------------------------------------------------------------------------------------------------- 14 Cu 1 2.439248537579902e-01 2.439248537519816e-01 6.00867e-12 4.10635e-11 2 9.730163921813649e-01 9.730163921579391e-01 2.34258e-11 3.53293e-11 3 -1.608123700202249e-01 -1.608123700044922e-01 1.57326e-11 1.72264e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 2.981312896544791e+00 2.981312896581348e+00 3.65565e-11 5.86399e-10 2 -1.424094816514643e+00 -1.424094816524958e+00 1.03155e-11 5.68235e-10 3 1.239371623656454e+00 1.239371623685231e+00 2.87765e-11 1.57649e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 1.345763412172423e+00 1.345763412163069e+00 9.35430e-12 3.70257e-11 2 2.082462405507010e+00 2.082462405499308e+00 7.70184e-12 6.81579e-11 3 1.631424906914146e+00 1.631424906914593e+00 4.46754e-13 2.12190e-10 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -6.766585305696186e-01 -6.766585305560163e-01 1.36022e-11 1.97541e-10 2 -6.174129904371436e-01 -6.174129904078821e-01 2.92615e-11 1.71036e-10 3 -4.965883431046165e-01 -4.965883431153343e-01 1.07178e-11 1.27076e-10 ----------------------------------------------------------------------------------------------------- 18 Cu 1 6.775175042373111e-01 6.775175042903158e-01 5.30047e-11 2.04055e-10 2 1.068562712654331e+00 1.068562712603189e+00 5.11420e-11 3.44644e-10 3 -2.710241155568017e-01 -2.710241154632767e-01 9.35250e-11 1.24499e-10 ----------------------------------------------------------------------------------------------------- 19 Cu 1 5.306008048667689e-01 5.306008048832280e-01 1.64592e-11 1.05484e-09 * 2 2.035763751892458e-01 2.035763752104153e-01 2.11695e-11 2.27010e-11 3 -2.419492710218856e-01 -2.419492710283745e-01 6.48898e-12 1.94721e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 1.573111303131652e-01 1.573111303019095e-01 1.12557e-11 2.01623e-10 2 1.159066818264686e+00 1.159066818277305e+00 1.26190e-11 6.86891e-11 3 2.442513824572234e-01 2.442513824485696e-01 8.65377e-12 5.37981e-11 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.981172193866320e+00 -1.981172193864613e+00 1.70775e-12 4.07741e-10 2 -1.312654416765097e-01 -1.312654416624545e-01 1.40551e-11 4.79338e-10 3 1.717357661688907e+00 1.717357661632152e+00 5.67553e-11 1.68989e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 1.133122712927557e+00 1.133122712923576e+00 3.98059e-12 4.54903e-11 2 3.124655769663092e+00 3.124655769652153e+00 1.09388e-11 2.85992e-10 3 2.741324899890887e+00 2.741324899865167e+00 2.57199e-11 4.36820e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -6.649646111274479e-01 -6.649646111170526e-01 1.03952e-11 1.64370e-09 * 2 4.975395682545483e-01 4.975395682443405e-01 1.02077e-11 1.23390e-10 3 -5.934433601268185e-01 -5.934433601357865e-01 8.96794e-12 1.97792e-11 ----------------------------------------------------------------------------------------------------- 24 Cu 1 4.480218339360497e-01 4.480218338572263e-01 7.88234e-11 2.42794e-09 * 2 -2.153418796843252e-01 -2.153418796615751e-01 2.27501e-11 2.11067e-10 3 -7.389793032863005e-01 -7.389793032857916e-01 5.08815e-13 1.19575e-10 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -1.820532568627401e+00 -1.820532568691720e+00 6.43188e-11 1.21547e-10 2 -1.111381174134191e+00 -1.111381174130459e+00 3.73213e-12 3.22558e-11 3 2.132987698535574e-01 2.132987698872013e-01 3.36439e-11 9.54093e-11 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -1.034976038030837e+00 -1.034976038041132e+00 1.02951e-11 4.12863e-10 2 1.595437501454990e+00 1.595437501379380e+00 7.56102e-11 3.27779e-10 3 -2.037243239288051e+00 -2.037243239154610e+00 1.33440e-10 1.96195e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 2.081308896599650e+00 2.081308896556937e+00 4.27134e-11 1.02816e-10 2 -3.762635119866125e+00 -3.762635119835648e+00 3.04774e-11 1.20806e-10 3 1.498109079713529e+00 1.498109079703137e+00 1.03912e-11 2.52781e-10 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -1.666025756569784e+00 -1.666025756574919e+00 5.13545e-12 1.40891e-10 2 1.770745316604530e+00 1.770745316608173e+00 3.64353e-12 1.64537e-11 3 -3.258037888136193e-01 -3.258037888121322e-01 1.48709e-12 9.09078e-12 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -1.050777142388507e+00 -1.050777142383438e+00 5.06883e-12 4.22248e-10 2 -9.031986415676250e-01 -9.031986415648654e-01 2.75957e-12 1.61723e-09 * 3 1.872393600021711e-01 1.872393600060303e-01 3.85914e-12 1.37571e-10 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -2.931839288904982e-01 -2.931839289236127e-01 3.31145e-11 1.61081e-10 2 8.245221858083661e-01 8.245221857918287e-01 1.65374e-11 2.08737e-10 3 5.521839558439482e-01 5.521839558548514e-01 1.09032e-11 6.29694e-11 ----------------------------------------------------------------------------------------------------- 31 Cu 1 7.780474723018163e-01 7.780474723088759e-01 7.05969e-12 2.09545e-10 2 -9.806248594076219e-01 -9.806248594083337e-01 7.11764e-13 2.14030e-10 3 7.261834480796441e-01 7.261834480872879e-01 7.64377e-12 3.10415e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 1.244235941975776e+00 1.244235942012202e+00 3.64260e-11 9.26874e-10 2 9.874480569611341e-01 9.874480569849838e-01 2.38497e-11 7.26100e-09 * 3 1.235876014029025e+00 1.235876014013501e+00 1.55247e-11 1.52073e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 9, direction = 1: |F_model - F_numer| error = ----------------------- = 3.92639e-10 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Zr | a0 = 4.532810211181641 | (Configuration in file "config-Zr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 -1.779406967158934e-01 -1.779406967210904e-01 5.19701e-12 1.54170e-10 2 2.385436965011643e-01 2.385436965130809e-01 1.19166e-11 5.98409e-10 3 -2.850116593139827e-01 -2.850116593052059e-01 8.77681e-12 7.09844e-11 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -1.356361570523687e-01 -1.356361570468418e-01 5.52694e-12 6.72243e-11 2 -2.702085043293886e-01 -2.702085043405235e-01 1.11349e-11 1.43839e-10 3 4.505985291858593e-01 4.505985291684527e-01 1.74066e-11 6.56714e-11 ----------------------------------------------------------------------------------------------------- 3 Zr 1 4.849612882612455e-01 4.849612882717796e-01 1.05341e-11 2.44974e-10 2 -4.978531045912238e-01 -4.978531046075419e-01 1.63181e-11 3.53161e-10 3 4.397619160092682e-01 4.397619160141946e-01 4.92639e-12 6.81244e-11 ----------------------------------------------------------------------------------------------------- 4 Zr 1 -5.990506727014459e-02 -5.990506727419511e-02 4.05052e-12 2.55973e-10 2 5.424218494137104e-01 5.424218493835169e-01 3.01935e-11 7.10418e-10 3 4.136670543095466e-02 4.136670545515326e-02 2.41986e-11 4.88518e-11 ----------------------------------------------------------------------------------------------------- 5 Zr 1 3.916886531713824e-01 3.916886531358764e-01 3.55060e-11 8.43319e-10 2 2.779131153122315e-01 2.779131153257637e-01 1.35322e-11 2.05675e-10 3 1.920918468850654e-01 1.920918468294755e-01 5.55899e-11 3.68350e-11 ----------------------------------------------------------------------------------------------------- 6 Zr 1 -7.597070983771723e-01 -7.597070983581498e-01 1.90226e-11 6.83703e-11 2 2.346971623297416e-01 2.346971623290690e-01 6.72601e-13 1.16018e-09 3 6.348209499009623e-01 6.348209499033151e-01 2.35278e-12 1.62679e-09 * ----------------------------------------------------------------------------------------------------- 7 Zr 1 5.585102920575338e-01 5.585102919687743e-01 8.87594e-11 3.45912e-10 2 -3.507605727617404e-01 -3.507605727796086e-01 1.78682e-11 1.22543e-10 3 -1.156591331476436e+00 -1.156591331467447e+00 8.98925e-12 3.72157e-10 ----------------------------------------------------------------------------------------------------- 8 Zr 1 1.217140373083438e+00 1.217140373077278e+00 6.15996e-12 9.99485e-10 2 5.148954255085720e-01 5.148954255476957e-01 3.91237e-11 2.52449e-09 * 3 -1.022393124501475e+00 -1.022393124496323e+00 5.15188e-12 2.75848e-09 * ----------------------------------------------------------------------------------------------------- 9 Zr 1 -8.923355930139699e-01 -8.923355930087641e-01 5.20584e-12 3.84048e-10 2 -1.496970576281986e+00 -1.496970576258686e+00 2.33009e-11 7.72822e-11 3 -1.041432884193578e+00 -1.041432884164006e+00 2.95721e-11 1.24505e-09 ----------------------------------------------------------------------------------------------------- 10 Zr 1 1.113064736755908e+00 1.113064736740631e+00 1.52771e-11 8.09914e-11 2 -3.793959628625685e-01 -3.793959628744670e-01 1.18985e-11 1.52497e-10 3 -1.631548573126333e-02 -1.631548572828956e-02 2.97377e-12 5.05221e-11 ----------------------------------------------------------------------------------------------------- 11 Zr 1 -1.445161121170185e+00 -1.445161121129432e+00 4.07525e-11 2.45340e-09 * 2 1.181722237466374e+00 1.181722237433649e+00 3.27249e-11 3.38398e-10 3 -2.495724367073216e+00 -2.495724367077574e+00 4.35829e-12 9.76348e-11 ----------------------------------------------------------------------------------------------------- 12 Zr 1 -7.297365005725553e-01 -7.297365006614859e-01 8.89305e-11 2.37723e-10 2 1.113418868472315e+00 1.113418868487247e+00 1.49329e-11 9.52967e-10 3 1.559433795615207e+00 1.559433795620957e+00 5.75051e-12 3.74860e-09 * ----------------------------------------------------------------------------------------------------- 13 Zr 1 9.517644254514473e-01 9.517644254555648e-01 4.11748e-12 1.76544e-10 2 4.040311067047569e-01 4.040311066840104e-01 2.07465e-11 2.93759e-10 3 1.003373573908925e+00 1.003373573953620e+00 4.46949e-11 1.73089e-10 ----------------------------------------------------------------------------------------------------- 14 Zr 1 -4.446162002561086e-01 -4.446162002537289e-01 2.37971e-12 2.51391e-10 2 -7.566222884518662e-01 -7.566222884676900e-01 1.58238e-11 6.80772e-10 3 4.420917985804345e-01 4.420917985573785e-01 2.30560e-11 8.23520e-11 ----------------------------------------------------------------------------------------------------- 15 Zr 1 -1.154963420689543e+00 -1.154963420669677e+00 1.98666e-11 5.62992e-11 2 9.684726899907466e-01 9.684726899806714e-01 1.00753e-11 1.53362e-10 3 -1.815256220666310e-01 -1.815256220507273e-01 1.59037e-11 3.96707e-10 ----------------------------------------------------------------------------------------------------- 16 Zr 1 4.770733046079216e-01 4.770733046395330e-01 3.16114e-11 1.55123e-10 2 -1.150169900165778e+00 -1.150169900180838e+00 1.50593e-11 9.11025e-11 3 -1.490082197781192e-01 -1.490082197674820e-01 1.06373e-11 1.20763e-09 ----------------------------------------------------------------------------------------------------- 17 Zr 1 -3.419498384288829e-01 -3.419498384254857e-01 3.39717e-12 3.22952e-10 2 2.547476143679188e-01 2.547476143588658e-01 9.05298e-12 5.70157e-11 3 -1.120146224918756e+00 -1.120146224926292e+00 7.53597e-12 1.88036e-10 ----------------------------------------------------------------------------------------------------- 18 Zr 1 -1.427680995436804e+00 -1.427680995473474e+00 3.66704e-11 2.74993e-10 2 -2.801409257110202e+00 -2.801409257127273e+00 1.70708e-11 9.64478e-10 3 2.217111751626241e+00 2.217111751598225e+00 2.80158e-11 1.99085e-09 * ----------------------------------------------------------------------------------------------------- 19 Zr 1 1.297694589945980e+00 1.297694589962271e+00 1.62919e-11 4.97338e-11 2 4.608999600358743e-02 4.608999601886419e-02 1.52768e-11 1.58443e-10 3 1.802907572868362e-01 1.802907572971197e-01 1.02835e-11 1.99272e-10 ----------------------------------------------------------------------------------------------------- 20 Zr 1 -7.878223483997381e-01 -7.878223483921697e-01 7.56839e-12 2.74038e-09 * 2 8.362870544048845e-01 8.362870543749579e-01 2.99266e-11 4.41640e-10 3 -4.949758738574352e-01 -4.949758738680944e-01 1.06592e-11 8.62074e-11 ----------------------------------------------------------------------------------------------------- 21 Zr 1 -1.189562083052570e+00 -1.189562083054795e+00 2.22489e-12 3.24094e-10 2 -1.008126950941708e-01 -1.008126951379829e-01 4.38121e-11 2.33059e-10 3 1.610066130232300e+00 1.610066130090231e+00 1.42069e-10 2.92373e-10 ----------------------------------------------------------------------------------------------------- 22 Zr 1 7.887258652605209e-01 7.887258652366869e-01 2.38340e-11 1.25873e-10 2 6.913643906438562e-01 6.913643906010335e-01 4.28227e-11 1.37255e-09 3 -1.066192273832512e+00 -1.066192273831922e+00 5.90639e-13 1.63618e-10 ----------------------------------------------------------------------------------------------------- 23 Zr 1 -8.944042187724269e-02 -8.944042188025768e-02 3.01499e-12 6.52377e-10 2 -1.080953624164569e-01 -1.080953624316991e-01 1.52422e-11 2.42359e-10 3 7.503836442734875e-02 7.503836441419533e-02 1.31534e-11 1.01337e-10 ----------------------------------------------------------------------------------------------------- 24 Zr 1 -1.301006741480352e-01 -1.301006741904017e-01 4.23665e-11 2.37562e-10 2 -2.084199386941840e-01 -2.084199387652467e-01 7.10627e-11 6.06247e-10 3 -2.879698924651746e-01 -2.879698924186486e-01 4.65260e-11 1.44967e-10 ----------------------------------------------------------------------------------------------------- 25 Zr 1 -3.672901622497150e-01 -3.672901622716843e-01 2.19693e-11 6.40756e-10 2 9.706945317425705e-03 9.706945302921939e-03 1.45038e-11 6.64383e-11 3 -4.852934336370085e-02 -4.852934336578257e-02 2.08172e-12 3.53507e-11 ----------------------------------------------------------------------------------------------------- 26 Zr 1 6.071771586249461e-01 6.071771586387522e-01 1.38061e-11 3.50892e-11 2 -5.468722322659630e-02 -5.468722321139221e-02 1.52041e-11 9.44336e-11 3 3.373787016199975e-01 3.373787016829153e-01 6.29178e-11 8.52648e-11 ----------------------------------------------------------------------------------------------------- 27 Zr 1 -4.409811729126734e-02 -4.409811731690807e-02 2.56407e-11 3.10287e-10 2 9.161364792754290e-02 9.161364791373265e-02 1.38102e-11 2.68649e-10 3 4.154583558722317e-01 4.154583558491209e-01 2.31107e-11 8.82404e-11 ----------------------------------------------------------------------------------------------------- 28 Zr 1 3.050018540435541e-01 3.050018540022233e-01 4.13307e-11 1.95700e-10 2 -8.140571029443111e-02 -8.140571029432107e-02 1.10037e-13 1.25372e-10 3 -2.582409534914346e-01 -2.582409535003035e-01 8.86891e-12 1.45104e-10 ----------------------------------------------------------------------------------------------------- 29 Zr 1 3.186348197099087e+00 3.186348196998537e+00 1.00549e-10 1.07163e-09 2 2.293166864250478e+00 2.293166864248685e+00 1.79234e-12 2.62679e-10 3 1.257569662855013e+00 1.257569662829632e+00 2.53801e-11 4.33136e-11 ----------------------------------------------------------------------------------------------------- 30 Zr 1 -6.497840733478030e-02 -6.497840735916427e-02 2.43840e-11 4.29162e-10 2 -6.224468035048569e-01 -6.224468035428152e-01 3.79583e-11 2.48081e-10 3 -7.107668391916944e-01 -7.107668391959419e-01 4.24749e-12 1.67433e-10 ----------------------------------------------------------------------------------------------------- 31 Zr 1 -2.786294035942793e-01 -2.786294035950319e-01 7.52509e-13 7.60682e-10 2 -4.225648521681125e-01 -4.225648521955012e-01 2.73887e-11 1.57148e-10 3 -4.122050518239904e-01 -4.122050518516976e-01 2.77072e-11 2.11170e-10 ----------------------------------------------------------------------------------------------------- 32 Zr 1 -8.575964314317074e-01 -8.575964314167478e-01 1.49596e-11 3.37731e-10 2 -3.972699126617419e-01 -3.972699126701525e-01 8.41055e-12 5.01505e-10 3 -1.094236923572441e-01 -1.094236923520289e-01 5.21520e-12 1.36827e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 25, direction = 2: |F_model - F_numer| error = ----------------------- = 1.49416e-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 = Cu Zr | a0 = 4.153991529098131 | (Configuration in file "config-CuZr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 -9.891596583416074e-01 -9.891596583433553e-01 1.74794e-12 8.13904e-12 2 1.233704570626843e+00 1.233704570620486e+00 6.35714e-12 1.75785e-10 3 5.952162600813986e-01 5.952162600773260e-01 4.07263e-12 6.56761e-11 ----------------------------------------------------------------------------------------------------- 2 Cu 1 1.344634909937397e+00 1.344634909954668e+00 1.72713e-11 4.75213e-11 2 -1.603283776066265e-01 -1.603283775384740e-01 6.81525e-11 2.22283e-10 3 6.236861061991800e-01 6.236861062176944e-01 1.85144e-11 5.54480e-11 ----------------------------------------------------------------------------------------------------- 3 Zr 1 1.834272339496362e+00 1.834272339490634e+00 5.72764e-12 1.01849e-10 2 1.039090105227198e+00 1.039090105227387e+00 1.89182e-13 1.68442e-10 3 -6.018952063531338e-01 -6.018952063373371e-01 1.57967e-11 9.87291e-11 ----------------------------------------------------------------------------------------------------- 4 Cu 1 6.485138356708186e-01 6.485138356891254e-01 1.83068e-11 4.47704e-11 2 -3.090690620397935e-01 -3.090690620022194e-01 3.75741e-11 5.75501e-11 3 -6.376300518374309e-01 -6.376300518386175e-01 1.18661e-12 1.69206e-09 * ----------------------------------------------------------------------------------------------------- 5 Zr 1 -2.151556859074792e+00 -2.151556859078061e+00 3.26894e-12 1.21676e-11 2 -2.497181722709571e-01 -2.497181722655812e-01 5.37592e-12 1.35913e-11 3 -6.167883381707158e-01 -6.167883381691438e-01 1.57196e-12 4.10654e-11 ----------------------------------------------------------------------------------------------------- 6 Zr 1 1.239978532136967e+00 1.239978532125099e+00 1.18678e-11 1.09657e-10 2 -6.834438167204847e-01 -6.834438167325904e-01 1.21056e-11 2.00313e-10 3 2.541569340980264e-01 2.541569340731906e-01 2.48357e-11 2.02978e-10 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.056742708168112e+00 1.056742708171017e+00 2.90479e-12 3.22764e-11 2 2.105225776533713e-01 2.105225776533312e-01 4.01068e-14 2.88597e-09 * 3 1.265559705529048e+00 1.265559705527748e+00 1.29985e-12 4.76521e-11 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -2.667798591758484e-01 -2.667798591756458e-01 2.02560e-13 4.97565e-10 2 -5.769936004369849e-01 -5.769936004364863e-01 4.98601e-13 9.61469e-11 3 6.591409424750311e-01 6.591409424667501e-01 8.28093e-12 2.02416e-10 ----------------------------------------------------------------------------------------------------- 9 Zr 1 3.788174582311075e-02 3.788174583871898e-02 1.56082e-11 2.09451e-10 2 -1.002910572628655e+00 -1.002910572664693e+00 3.60376e-11 2.77179e-10 3 1.398833113984255e-03 1.398833118086955e-03 4.10270e-12 9.31314e-11 ----------------------------------------------------------------------------------------------------- 10 Cu 1 4.403741095696595e-01 4.403741095525251e-01 1.71344e-11 3.55802e-11 2 -5.769711086898642e-01 -5.769711086729470e-01 1.69172e-11 8.04159e-11 3 -5.057861407129383e-02 -5.057861407100176e-02 2.92065e-13 1.17431e-10 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -5.736738186942538e-01 -5.736738186848506e-01 9.40326e-12 1.13421e-10 2 -4.963441075634469e-01 -4.963441076184667e-01 5.50198e-11 5.34710e-11 3 -2.978647425736234e-01 -2.978647425940618e-01 2.04384e-11 1.51084e-10 ----------------------------------------------------------------------------------------------------- 12 Zr 1 1.353764525485963e-01 1.353764525222658e-01 2.63304e-11 1.07475e-10 2 -2.235098642616865e-01 -2.235098642893082e-01 2.76217e-11 1.30677e-09 3 8.535256735682091e-01 8.535256735558210e-01 1.23881e-11 5.92165e-10 ----------------------------------------------------------------------------------------------------- 13 Zr 1 -2.815297356144055e+00 -2.815297356161873e+00 1.78173e-11 2.74234e-11 2 4.632973709959551e-01 4.632973710253314e-01 2.93763e-11 1.42330e-10 3 -1.021676104663195e+00 -1.021676104685275e+00 2.20801e-11 7.75868e-11 ----------------------------------------------------------------------------------------------------- 14 Zr 1 1.812889904348410e+00 1.812889904351745e+00 3.33511e-12 2.38523e-09 * 2 2.208143061992262e+00 2.208143061996032e+00 3.77076e-12 2.26958e-10 3 -8.398558680654551e-01 -8.398558680661128e-01 6.57696e-13 2.21716e-09 * ----------------------------------------------------------------------------------------------------- 15 Cu 1 7.543945614127175e-01 7.543945613548322e-01 5.78854e-11 9.24256e-11 2 -1.682655064954837e+00 -1.682655064941697e+00 1.31393e-11 6.38643e-10 3 1.676925163692982e+00 1.676925163691901e+00 1.08091e-12 1.03515e-10 ----------------------------------------------------------------------------------------------------- 16 Zr 1 -1.134993488772626e+00 -1.134993488794414e+00 2.17883e-11 2.60937e-10 2 8.066560457338513e-02 8.066560459887252e-02 2.54874e-11 1.42504e-10 3 1.232195907182351e+00 1.232195907167962e+00 1.43892e-11 1.48176e-10 ----------------------------------------------------------------------------------------------------- 17 Zr 1 -3.650935744724806e-01 -3.650935744787475e-01 6.26688e-12 8.10779e-11 2 1.515757264092856e+00 1.515757264054908e+00 3.79485e-11 1.97359e-10 3 5.532353356907426e-01 5.532353356874953e-01 3.24729e-12 2.42147e-09 * ----------------------------------------------------------------------------------------------------- 18 Cu 1 -1.523001489810894e-01 -1.523001489646261e-01 1.64634e-11 4.00021e-10 2 -1.233567919009814e+00 -1.233567919004839e+00 4.97535e-12 4.24137e-09 * 3 -5.678276629335746e-01 -5.678276629327786e-01 7.95919e-13 1.24880e-09 ----------------------------------------------------------------------------------------------------- 19 Cu 1 -2.046251445366931e-02 -2.046251446202828e-02 8.35897e-12 5.41617e-10 2 7.514084332198179e-01 7.514084332280025e-01 8.18468e-12 2.17592e-09 * 3 -6.507691370006640e-01 -6.507691370035483e-01 2.88436e-12 8.80563e-11 ----------------------------------------------------------------------------------------------------- 20 Cu 1 7.653838436394444e-01 7.653838436668282e-01 2.73838e-11 4.99337e-11 2 1.465757717371817e-01 1.465757717461654e-01 8.98376e-12 2.09672e-10 3 -1.010201737391322e+00 -1.010201737368931e+00 2.23914e-11 1.89609e-09 * ----------------------------------------------------------------------------------------------------- 21 Zr 1 -9.991790447069460e-01 -9.991790446950477e-01 1.18983e-11 1.59344e-09 * 2 6.738811574949402e-01 6.738811574813031e-01 1.36371e-11 1.91076e-09 * 3 -9.056652364340851e-01 -9.056652364370242e-01 2.93909e-12 4.46956e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 -6.244549903271872e-01 -6.244549903147190e-01 1.24682e-11 8.99174e-10 2 2.395380234411740e-01 2.395380234111872e-01 2.99868e-11 1.52065e-10 3 3.399671328400571e-02 3.399671331920096e-02 3.51952e-11 2.98993e-10 ----------------------------------------------------------------------------------------------------- 23 Zr 1 1.148626284045809e+00 1.148626284066642e+00 2.08324e-11 8.43730e-11 2 -5.828615084906211e-01 -5.828615085285394e-01 3.79182e-11 2.15958e-10 3 8.166077873603094e-01 8.166077874087536e-01 4.84442e-11 1.52341e-10 ----------------------------------------------------------------------------------------------------- 24 Zr 1 -2.376246672373573e-01 -2.376246672327423e-01 4.61503e-12 3.71092e-10 2 4.437870642791654e-01 4.437870642302756e-01 4.88898e-11 9.20223e-10 3 -8.456466984276597e-01 -8.456466984111183e-01 1.65414e-11 2.07674e-11 ----------------------------------------------------------------------------------------------------- 25 Zr 1 3.376338164871140e-01 3.376338164959001e-01 8.78614e-12 1.23299e-10 2 -3.699705140587344e-01 -3.699705140796581e-01 2.09237e-11 2.00969e-09 * 3 1.573888834572307e+00 1.573888834574035e+00 1.72795e-12 4.39986e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 6.891402534902030e-02 6.891402533958235e-02 9.43795e-12 2.72360e-10 2 -4.463867945944041e-01 -4.463867945948407e-01 4.36540e-13 2.67094e-10 3 -3.266039413563299e-01 -3.266039413302826e-01 2.60473e-11 4.13982e-11 ----------------------------------------------------------------------------------------------------- 27 Cu 1 -1.252126675622556e-01 -1.252126675599107e-01 2.34490e-12 2.66896e-11 2 6.984778726613809e-01 6.984778726572802e-01 4.10072e-12 1.85833e-10 3 -4.633921772405201e-02 -4.633921773544766e-02 1.13956e-11 5.16784e-10 ----------------------------------------------------------------------------------------------------- 28 Cu 1 4.415305243594064e-01 4.415305243663101e-01 6.90370e-12 1.05238e-10 2 -6.452196640886532e-01 -6.452196640671237e-01 2.15294e-11 7.49196e-11 3 -6.507179156079551e-01 -6.507179156013133e-01 6.64180e-12 6.47783e-11 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -1.197659414777135e+00 -1.197659414806756e+00 2.96205e-11 3.44091e-10 2 3.740166299904088e-02 3.740166299313878e-02 5.90210e-12 4.10051e-10 3 -6.309284892713791e-01 -6.309284892544453e-01 1.69338e-11 2.36228e-10 ----------------------------------------------------------------------------------------------------- 30 Zr 1 -7.876034652983921e-01 -7.876034653044690e-01 6.07692e-12 3.48037e-10 2 1.630268163967535e-01 1.630268163458646e-01 5.08889e-11 7.42607e-11 3 -5.809465479152510e-01 -5.809465479104423e-01 4.80871e-12 3.64014e-11 ----------------------------------------------------------------------------------------------------- 31 Zr 1 1.463293952216787e+00 1.463293952221682e+00 4.89497e-12 1.14696e-10 2 -1.266882643065088e+00 -1.266882643074469e+00 9.38094e-12 2.61888e-10 3 8.117813858571615e-01 8.117813858249588e-01 3.22027e-11 1.50686e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 -1.089390017190036e+00 -1.089390017190835e+00 7.98916e-13 2.62044e-10 2 6.015554330893256e-01 6.015554330994846e-01 1.01590e-11 1.45850e-10 3 -6.693800729076174e-01 -6.693800728999312e-01 7.68619e-12 1.42820e-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 = 9, direction = 3: |F_model - F_numer| error = ----------------------- = 2.93294e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.93294e-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 2.93294e-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.