!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : EAM_Dynamo_LiuLiuBorucki_1999_AlCu__MO_020851069572_000 Supported species : Al Cu 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 = Al | a0 = 4.03207302094 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 1.356744893501621e-01 1.356744893316739e-01 1.84883e-11 4.43110e-10 2 -1.115223566794971e-01 -1.115223566774345e-01 2.06259e-12 1.37580e-09 3 -3.910164983937063e-01 -3.910164984397958e-01 4.60895e-11 2.32799e-10 ----------------------------------------------------------------------------------------------------- 2 Al 1 -4.401625188324886e-01 -4.401625188551717e-01 2.26831e-11 3.45086e-10 2 9.114597765048297e-01 9.114597765140158e-01 9.18610e-12 8.48591e-11 3 6.051822558481496e-01 6.051822558412441e-01 6.90548e-12 2.52145e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 4.989970316516480e-01 4.989970317148879e-01 6.32398e-11 1.55736e-09 2 6.006927156916666e-01 6.006927154621783e-01 2.29488e-10 8.14262e-10 3 8.907457891478145e-01 8.907457891318911e-01 1.59235e-11 2.78876e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 8.005687820551989e-01 8.005687821582910e-01 1.03092e-10 7.89159e-10 2 5.184933124386772e-01 5.184933124298121e-01 8.86513e-12 2.00093e-09 3 9.267422084118307e-01 9.267422084126308e-01 8.00027e-13 3.04086e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 3.942403666962465e-01 3.942403666258790e-01 7.03675e-11 3.01416e-09 2 -4.147672489666231e-02 -4.147672486601254e-02 3.06498e-11 8.27375e-10 3 2.089929454982605e-01 2.089929455504750e-01 5.22145e-11 1.76608e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -6.609178860445539e-01 -6.609178860589207e-01 1.43667e-11 1.17272e-10 2 4.570903917024544e-01 4.570903917330710e-01 3.06167e-11 1.11494e-10 3 5.908067642130979e-01 5.908067642698650e-01 5.67671e-11 1.99019e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 6.512048426012359e-01 6.512048426252737e-01 2.40378e-11 4.38738e-10 2 -1.913495600882704e+00 -1.913495600864935e+00 1.77689e-11 2.67894e-10 3 -2.185669765477793e+00 -2.185669765452201e+00 2.55929e-11 9.46106e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 -1.828039422117266e+00 -1.828039421951455e+00 1.65811e-10 7.26633e-10 2 -6.461643224555021e-01 -6.461643220619833e-01 3.93519e-10 1.11258e-09 3 -5.242531584386865e-01 -5.242531584047004e-01 3.39860e-11 5.48763e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 -1.262325059796505e-02 -1.262325055995833e-02 3.80067e-11 6.22250e-09 2 -1.866569624180265e+00 -1.866569624179894e+00 3.70814e-13 3.41813e-10 3 -1.602229680020198e+00 -1.602229680075838e+00 5.56390e-11 2.02709e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -7.608718054234803e-01 -7.608718054254959e-01 2.01561e-12 2.70206e-10 2 9.714806246979762e-01 9.714806246665840e-01 3.13922e-11 1.39466e-09 3 -1.232552766065858e+00 -1.232552766077914e+00 1.20568e-11 7.67069e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 -1.354528715296359e-01 -1.354528714241999e-01 1.05436e-10 2.53745e-10 2 -1.599624021859638e+00 -1.599624021828235e+00 3.14031e-11 2.07199e-09 3 1.208652333926745e+00 1.208652333890924e+00 3.58205e-11 1.66067e-11 ----------------------------------------------------------------------------------------------------- 12 Al 1 2.666841972890886e-01 2.666841971979061e-01 9.11825e-11 5.22782e-08 * 2 1.354611874444559e+00 1.354611874432325e+00 1.22347e-11 1.67507e-09 3 1.753547929550533e+00 1.753547929492670e+00 5.78628e-11 1.09392e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -8.434387627084448e-01 -8.434387627867155e-01 7.82707e-11 4.91421e-09 2 -1.842177476471947e+00 -1.842177476479367e+00 7.41962e-12 9.91253e-09 * 3 -2.313321528890161e+00 -2.313321528919093e+00 2.89320e-11 6.86026e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 8.646026062979274e-02 8.646026058096917e-02 4.88236e-11 6.03844e-11 2 6.347038444729766e-01 6.347038444590748e-01 1.39018e-11 4.38830e-11 3 -9.094624861009373e-02 -9.094624863546288e-02 2.53692e-11 1.22078e-10 ----------------------------------------------------------------------------------------------------- 15 Al 1 2.142610817881135e+00 2.142610817840751e+00 4.03846e-11 1.78527e-08 * 2 -9.558849337816292e-01 -9.558849337548000e-01 2.68292e-11 6.90306e-10 3 1.190770985612517e+00 1.190770985642547e+00 3.00298e-11 5.57500e-09 ----------------------------------------------------------------------------------------------------- 16 Al 1 8.604191107367684e-01 8.604191107777284e-01 4.09600e-11 9.15852e-10 2 1.680960829680726e+00 1.680960829545292e+00 1.35434e-10 1.38747e-09 3 1.173805060526457e+00 1.173805060524045e+00 2.41140e-12 9.22284e-11 ----------------------------------------------------------------------------------------------------- 17 Al 1 -5.051074874690317e-01 -5.051074874083109e-01 6.07208e-11 1.74103e-10 2 2.311989269380431e-01 2.311989269141776e-01 2.38655e-11 3.87615e-09 3 -9.835664049713390e-01 -9.835664049238584e-01 4.74806e-11 7.08643e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 4.450945160766733e-01 4.450945160177149e-01 5.89584e-11 3.38268e-09 2 1.149955941824384e+00 1.149955941837519e+00 1.31350e-11 4.46579e-09 3 -1.504456972828975e+00 -1.504456972875870e+00 4.68956e-11 2.09064e-10 ----------------------------------------------------------------------------------------------------- 19 Al 1 9.505863080876634e-01 9.505863081141510e-01 2.64876e-11 5.27693e-11 2 -4.843883599595292e-01 -4.843883599560331e-01 3.49615e-12 2.69488e-10 3 7.280018733829606e-01 7.280018732979479e-01 8.50128e-11 3.16778e-08 * ----------------------------------------------------------------------------------------------------- 20 Al 1 3.024554050056452e-01 3.024554050302947e-01 2.46494e-11 4.82798e-11 2 6.129384366920805e-01 6.129384369424584e-01 2.50378e-10 2.20176e-10 3 -2.490458243176106e-01 -2.490458242960061e-01 2.16046e-11 5.07967e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -2.099028386691300e+00 -2.099028386687536e+00 3.76410e-12 1.04746e-10 2 -2.536789767635055e-01 -2.536789769260327e-01 1.62527e-10 2.09934e-10 3 3.254723364217234e-01 3.254723364368022e-01 1.50788e-11 3.57125e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 7.136139970373445e-01 7.136139971454034e-01 1.08059e-10 3.28182e-10 2 2.927197247028564e+00 2.927197246346621e+00 6.81943e-10 1.19652e-08 * 3 1.465119376218656e+00 1.465119376452947e+00 2.34291e-10 2.74558e-09 ----------------------------------------------------------------------------------------------------- 23 Al 1 3.482802944882575e-02 3.482802946762877e-02 1.88030e-11 2.20431e-10 2 7.255784673494367e-02 7.255784673406125e-02 8.82419e-13 2.23493e-10 3 6.128617575977953e-01 6.128617576096089e-01 1.18137e-11 2.73716e-10 ----------------------------------------------------------------------------------------------------- 24 Al 1 1.684794101314983e-01 1.684794101240163e-01 7.48196e-12 6.41055e-11 2 3.859841408418020e-01 3.859841408380245e-01 3.77753e-12 2.42638e-10 3 -5.195134067213659e-01 -5.195134067408599e-01 1.94940e-11 3.85160e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -1.642723238584306e+00 -1.642723238473893e+00 1.10413e-10 2.66960e-11 2 -1.241365145239072e+00 -1.241365145181771e+00 5.73017e-11 4.26867e-09 3 -1.208487553869714e+00 -1.208487553857192e+00 1.25229e-11 1.38369e-09 ----------------------------------------------------------------------------------------------------- 26 Al 1 -5.353121228341260e-01 -5.353121228192045e-01 1.49215e-11 2.86370e-09 2 1.395081916228163e+00 1.395081917365008e+00 1.13684e-09 4.24164e-09 3 -1.473790825568190e+00 -1.473790824246050e+00 1.32214e-09 1.93791e-09 ----------------------------------------------------------------------------------------------------- 27 Al 1 1.874929779447474e+00 1.874929779527773e+00 8.02993e-11 1.21449e-09 2 -2.993975796250227e+00 -2.993975797557142e+00 1.30692e-09 1.24885e-08 * 3 1.477869021976471e+00 1.477869021529110e+00 4.47360e-10 7.64021e-09 * ----------------------------------------------------------------------------------------------------- 28 Al 1 -1.002625171179034e+00 -1.002625171192036e+00 1.30018e-11 9.77942e-11 2 1.143436795736666e+00 1.143436795739915e+00 3.24940e-12 1.92375e-08 * 3 -9.457810392558003e-02 -9.457810383939223e-02 8.61878e-11 1.23681e-10 ----------------------------------------------------------------------------------------------------- 29 Al 1 -1.010021621913100e+00 -1.010021621991718e+00 7.86173e-11 1.58311e-10 2 -1.049260726622670e+00 -1.049260726672124e+00 4.94540e-11 1.40027e-08 * 3 2.087715317814374e-01 2.087715319074999e-01 1.26063e-10 9.09032e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -2.365609219846849e-01 -2.365609220210417e-01 3.63569e-11 1.12038e-09 2 9.885895895481588e-01 9.885895895745926e-01 2.64339e-11 3.16744e-10 3 -6.147781758631565e-01 -6.147781759318249e-01 6.86684e-11 9.18987e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 5.453755854758513e-01 5.453755854686000e-01 7.25131e-12 1.86415e-10 2 -1.676602627448513e+00 -1.676602627689158e+00 2.40645e-10 2.26168e-08 * 3 9.233216376934079e-01 9.233216383719179e-01 6.78510e-10 1.65917e-08 * ----------------------------------------------------------------------------------------------------- 32 Al 1 8.406625383071655e-01 8.406625384068264e-01 9.96608e-11 2.16775e-09 2 6.397524822846897e-01 6.397524823188260e-01 3.41362e-11 3.08549e-10 3 6.975431061545726e-01 6.975431061274858e-01 2.70868e-11 5.66592e-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 dicontinuities. Maximum error obtained for particle = 9, direction = 1: |F_model - F_numer| error = ----------------------- = 3.01085e-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 = Cu | a0 = 3.61499977112 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 9.450000223973530e-01 9.450000224068120e-01 9.45899e-12 3.46480e-10 2 1.022464085824559e+00 1.022464085822191e+00 2.36788e-12 2.81616e-10 3 7.500761911557976e-01 7.500761911588543e-01 3.05667e-12 3.06109e-09 * ----------------------------------------------------------------------------------------------------- 2 Cu 1 -5.471992725064677e-01 -5.471992724828989e-01 2.35688e-11 4.23576e-11 2 -4.042710296308865e-01 -4.042710296316203e-01 7.33802e-13 1.83299e-10 3 2.663748491412404e-01 2.663748491410051e-01 2.35256e-13 2.58042e-10 ----------------------------------------------------------------------------------------------------- 3 Cu 1 -7.922553860640207e-01 -7.922553861313795e-01 6.73588e-11 9.18019e-11 2 -2.512812500038675e-01 -2.512812499101939e-01 9.36736e-11 5.41219e-10 3 5.820765298170516e-01 5.820765298638879e-01 4.68363e-11 6.48855e-09 * ----------------------------------------------------------------------------------------------------- 4 Cu 1 -4.683849680757246e-01 -4.683849681323863e-01 5.66617e-11 9.92606e-11 2 -1.028602433292134e+00 -1.028602433232751e+00 5.93829e-11 1.47293e-10 3 -2.737991451317737e-01 -2.737991451189061e-01 1.28677e-11 3.93555e-11 ----------------------------------------------------------------------------------------------------- 5 Cu 1 -3.319976018886403e-01 -3.319976018926635e-01 4.02317e-12 3.25297e-10 2 4.588668171711118e-01 4.588668170307382e-01 1.40374e-10 8.28690e-10 3 6.416907566413773e-03 6.416907632730215e-03 6.63164e-11 5.88332e-10 ----------------------------------------------------------------------------------------------------- 6 Cu 1 3.501639511924793e-01 3.501639511871196e-01 5.35971e-12 4.82331e-10 2 2.162236889009113e+00 2.162236889013961e+00 4.84812e-12 2.76214e-10 3 -1.755154635974067e+00 -1.755154635963887e+00 1.01799e-11 3.73056e-10 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.857009072551808e-02 1.857009074080622e-02 1.52881e-11 1.79333e-10 2 -2.792050093432038e+00 -2.792050093464076e+00 3.20384e-11 1.81538e-10 3 1.251031353648033e+00 1.251031353706744e+00 5.87108e-11 2.13920e-10 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -4.824035214543139e-01 -4.824035214903408e-01 3.60269e-11 1.01646e-10 2 3.788252706784072e-01 3.788252706823309e-01 3.92375e-12 6.94436e-10 3 9.255882800923294e-01 9.255882801849464e-01 9.26170e-11 2.80639e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 9.361219175409246e-01 9.361219175753788e-01 3.44542e-11 4.07816e-11 2 3.951340819857426e-01 3.951340820114475e-01 2.57049e-11 6.64170e-11 3 7.337120418448554e-01 7.337120418213736e-01 2.34818e-11 2.70084e-10 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -1.116743784907486e-01 -1.116743785078266e-01 1.70780e-11 3.56335e-10 2 -1.116634573971078e+00 -1.116634573921985e+00 4.90932e-11 9.09224e-11 3 1.212951119250633e+00 1.212951119229625e+00 2.10076e-11 5.98786e-09 * ----------------------------------------------------------------------------------------------------- 11 Cu 1 -4.227864676000936e-02 -4.227864671687408e-02 4.31353e-11 1.32464e-09 2 1.784378537916782e+00 1.784378537853204e+00 6.35787e-11 6.16300e-10 3 -1.595210585533083e+00 -1.595210585496529e+00 3.65534e-11 1.38844e-09 ----------------------------------------------------------------------------------------------------- 12 Cu 1 1.371930190974795e+00 1.371930190976484e+00 1.68887e-12 3.44017e-10 2 -1.279280041624703e+00 -1.279280041609155e+00 1.55485e-11 9.32430e-11 3 6.158172464578501e-02 6.158172462876879e-02 1.70162e-11 4.58070e-10 ----------------------------------------------------------------------------------------------------- 13 Cu 1 5.374874383638119e-01 5.374874383733923e-01 9.58045e-12 1.65272e-10 2 1.318272824698416e+00 1.318272824716809e+00 1.83928e-11 1.89721e-10 3 3.182682408283639e-01 3.182682407993468e-01 2.90171e-11 9.86906e-11 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -1.101735609040130e+00 -1.101735609090596e+00 5.04652e-11 6.80995e-10 2 -7.259289771982431e-01 -7.259289771998640e-01 1.62093e-12 6.91175e-11 3 8.674069969770619e-01 8.674069969610680e-01 1.59939e-11 7.50831e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 1.292898049257981e+00 1.292898049322505e+00 6.45237e-11 1.37304e-10 2 -7.126789713085221e-01 -7.126789713096540e-01 1.13187e-12 1.88996e-10 3 -2.782746484251573e+00 -2.782746484252486e+00 9.13047e-13 4.49562e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 6.128810733612482e-01 6.128810733304128e-01 3.08354e-11 5.79829e-10 2 -3.169292400290165e-01 -3.169292400646855e-01 3.56690e-11 2.03589e-10 3 -2.116158241346024e+00 -2.116158241208469e+00 1.37555e-10 4.80993e-10 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -4.283225913143261e-01 -4.283225913158075e-01 1.48143e-12 1.18628e-10 2 3.018347734947990e-01 3.018347734914666e-01 3.33239e-12 2.19792e-10 3 -1.001887636874561e+00 -1.001887636849933e+00 2.46276e-11 1.94641e-10 ----------------------------------------------------------------------------------------------------- 18 Cu 1 7.694238378033574e-01 7.694238377832439e-01 2.01136e-11 4.08155e-10 2 -1.083082600616322e+00 -1.083082600618099e+00 1.77725e-12 2.22051e-10 3 -1.441377224327355e-01 -1.441377224731373e-01 4.04018e-11 6.34032e-09 * ----------------------------------------------------------------------------------------------------- 19 Cu 1 -6.158687418339737e-01 -6.158687418495917e-01 1.56181e-11 2.20820e-10 2 4.155232619218659e-01 4.155232619565624e-01 3.46965e-11 7.19483e-10 3 1.864179135257018e+00 1.864179135256063e+00 9.54348e-13 1.67992e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 1.072330263582687e+00 1.072330263541015e+00 4.16727e-11 4.09351e-10 2 3.498811073874867e-01 3.498811074407374e-01 5.32506e-11 4.05775e-10 3 -8.428543598976020e-01 -8.428543599198550e-01 2.22530e-11 4.48372e-11 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.004501632072953e+00 -1.004501632057353e+00 1.56000e-11 4.56968e-11 2 -3.824767472982625e-01 -3.824767473188587e-01 2.05962e-11 2.48924e-10 3 -2.956581624839736e+00 -2.956581624802025e+00 3.77112e-11 1.15470e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 4.654463248833955e-01 4.654463248882241e-01 4.82858e-12 9.62889e-11 2 1.942749568492973e+00 1.942749568523417e+00 3.04443e-11 1.01241e-10 3 3.173592955900369e-01 3.173592955521713e-01 3.78656e-11 2.36058e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 1.856027258894632e+00 1.856027258899076e+00 4.44356e-12 7.09177e-11 2 -4.074033674950006e-01 -4.074033674986673e-01 3.66673e-12 4.86869e-09 * 3 1.969956971854185e+00 1.969956971859980e+00 5.79448e-12 1.01916e-10 ----------------------------------------------------------------------------------------------------- 24 Cu 1 2.116400083674849e-01 2.116400083740363e-01 6.55145e-12 4.90533e-10 2 -5.650435381737910e-01 -5.650435382084715e-01 3.46805e-11 7.38345e-10 3 -3.206809608432596e-01 -3.206809608291230e-01 1.41366e-11 5.17195e-11 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -3.882755322599780e-01 -3.882755322598797e-01 9.83658e-14 1.21460e-10 2 5.334455708779549e-01 5.334455708872616e-01 9.30678e-12 1.73017e-10 3 2.278379125097058e-01 2.278379125198254e-01 1.01196e-11 3.82032e-11 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -1.013195345406551e+00 -1.013195345416041e+00 9.49085e-12 2.15364e-10 2 -6.801560313001146e-01 -6.801560313025037e-01 2.38909e-12 5.61616e-11 3 1.161156847183486e+00 1.161156847040459e+00 1.43027e-10 1.06342e-09 ----------------------------------------------------------------------------------------------------- 27 Cu 1 -1.232587865024350e+00 -1.232587865106543e+00 8.21931e-11 1.13757e-10 2 1.970994736349557e+00 1.970994736308336e+00 4.12215e-11 9.58968e-11 3 1.545518941347512e-02 1.545518953933173e-02 1.25857e-10 3.67676e-11 ----------------------------------------------------------------------------------------------------- 28 Cu 1 6.901402176851160e-01 6.901402176808116e-01 4.30445e-12 1.40180e-10 2 -6.221215154969912e-01 -6.221215154701911e-01 2.68001e-11 9.54438e-11 3 -5.200678272485943e-01 -5.200678271812340e-01 6.73603e-11 1.16097e-10 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -2.181856158847718e+00 -2.181856158822043e+00 2.56755e-11 5.35725e-09 * 2 -1.049560317518365e+00 -1.049560317595392e+00 7.70271e-11 7.19385e-10 3 2.466643886147951e+00 2.466643886126921e+00 2.10298e-11 5.30358e-11 ----------------------------------------------------------------------------------------------------- 30 Cu 1 6.183522485710113e-01 6.183522485712897e-01 2.78333e-13 8.35515e-11 2 1.235548428959529e+00 1.235548428983207e+00 2.36782e-11 4.14230e-10 3 1.343700062174641e+00 1.343700062172396e+00 2.24420e-12 9.81120e-11 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -7.340233742923186e-01 -7.340233743326098e-01 4.02912e-11 1.85847e-10 2 2.909031496136617e-01 2.909031495922162e-01 2.14455e-11 4.65524e-11 3 -1.030629847050640e+00 -1.030629847099799e+00 4.91585e-11 6.45320e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 -2.718522682695724e-01 -2.718522682840608e-01 1.44884e-11 5.95218e-10 2 -1.143558375992623e+00 -1.143558376016627e+00 2.40046e-11 2.47596e-10 3 -1.001864463674415e+00 -1.001864463653101e+00 2.13141e-11 2.56456e-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 dicontinuities. Maximum error obtained for particle = 5, direction = 3: |F_model - F_numer| error = ----------------------- = 1.03346e-08 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 = Al Cu | a0 = 3.6614032196 | (Configuration in file "config-AlCu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 -1.578701591903310e+00 -1.578701591903562e+00 2.52021e-13 3.17878e-10 2 -6.038328579628802e-01 -6.038328580601533e-01 9.72731e-11 3.30894e-10 3 -9.746298323371362e-02 -9.746298323192404e-02 1.78958e-12 6.63943e-11 ----------------------------------------------------------------------------------------------------- 2 Al 1 1.419428542967791e+00 1.419428542970049e+00 2.25819e-12 1.68255e-10 2 3.738813266316521e+00 3.738813266295297e+00 2.12239e-11 2.61531e-10 3 -2.274357826141643e+00 -2.274357826130384e+00 1.12585e-11 1.08045e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 7.998620736580175e-01 7.998620736687067e-01 1.06891e-11 7.09397e-10 2 -2.865223929119624e+00 -2.865223929082292e+00 3.73315e-11 3.31965e-10 3 2.907731357682178e+00 2.907731357706234e+00 2.40559e-11 3.15903e-10 ----------------------------------------------------------------------------------------------------- 4 Cu 1 1.393573008600404e-01 1.393573008005692e-01 5.94712e-11 2.93305e-09 2 -6.775063894372968e-01 -6.775063894222386e-01 1.50582e-11 1.40671e-11 3 -9.857839519837400e-01 -9.857839519509616e-01 3.27784e-11 8.56585e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 -1.414688617772418e+00 -1.414688617783912e+00 1.14935e-11 3.57935e-10 2 -9.254205596948493e-01 -9.254205596502275e-01 4.46218e-11 1.74406e-10 3 6.591718297791033e-01 6.591718297610714e-01 1.80319e-11 5.46554e-11 ----------------------------------------------------------------------------------------------------- 6 Cu 1 6.494011317390117e-01 6.494011317393192e-01 3.07532e-13 1.72457e-10 2 1.640013066129006e+00 1.640013066111636e+00 1.73701e-11 2.15851e-10 3 7.659332402406928e-01 7.659332402403828e-01 3.09974e-13 5.15861e-10 ----------------------------------------------------------------------------------------------------- 7 Al 1 9.763961774932254e-01 9.763961775405424e-01 4.73170e-11 1.21731e-09 2 5.043710542545727e-01 5.043710542628956e-01 8.32290e-12 4.96483e-10 3 -1.391314093689649e+00 -1.391314093703523e+00 1.38740e-11 4.10168e-10 ----------------------------------------------------------------------------------------------------- 8 Al 1 1.558604299345896e+00 1.558604299377724e+00 3.18279e-11 5.58230e-10 2 1.045708514556908e+00 1.045708514290392e+00 2.66515e-10 8.50962e-08 * 3 -8.275297384413948e-01 -8.275297383936128e-01 4.77820e-11 6.10304e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 8.493725957621709e-01 8.493725957838856e-01 2.17146e-11 4.12304e-10 2 6.235501802204532e-01 6.235501801804139e-01 4.00393e-11 2.56945e-10 3 1.302642554840886e+00 1.302642554999052e+00 1.58167e-10 2.53799e-10 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -1.743823638679170e+00 -1.743823638732905e+00 5.37348e-11 1.27399e-09 2 -2.684813374523321e-01 -2.684813374695607e-01 1.72286e-11 7.05243e-10 3 -1.198311095437157e+00 -1.198311095452107e+00 1.49498e-11 2.15826e-07 * ----------------------------------------------------------------------------------------------------- 11 Cu 1 -8.426520055518871e-01 -8.426520055366037e-01 1.52834e-11 3.44172e-10 2 -1.866885141053794e+00 -1.866885141103368e+00 4.95735e-11 6.32928e-10 3 -1.024488718087811e+00 -1.024488718095434e+00 7.62324e-12 4.28232e-10 ----------------------------------------------------------------------------------------------------- 12 Cu 1 -2.519069382631277e-01 -2.519069382866563e-01 2.35286e-11 6.75766e-10 2 -4.036377785132674e-01 -4.036377785821360e-01 6.88685e-11 2.11083e-10 3 -9.278177165364053e-01 -9.278177165730263e-01 3.66209e-11 1.63589e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 1.930709695358477e-01 1.930709695216853e-01 1.41624e-11 1.16619e-09 2 -9.962667240747373e-01 -9.962667240590070e-01 1.57303e-11 4.20072e-10 3 -7.037443931543538e-01 -7.037443932478424e-01 9.34887e-11 1.45748e-09 ----------------------------------------------------------------------------------------------------- 14 Cu 1 2.522582892274099e-01 2.522582892282444e-01 8.34499e-13 1.26537e-10 2 1.171797031936883e+00 1.171797031935386e+00 1.49680e-12 4.99510e-10 3 -1.420297865027637e+00 -1.420297865020616e+00 7.02172e-12 1.81066e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 -5.630832941820971e-01 -5.630832941581937e-01 2.39034e-11 7.45286e-11 2 -1.780347439008275e+00 -1.780347439014506e+00 6.23013e-12 7.22157e-10 3 1.624657337272891e+00 1.624657337308458e+00 3.55664e-11 1.12302e-09 ----------------------------------------------------------------------------------------------------- 16 Al 1 1.351386698959626e+00 1.351386698900300e+00 5.93254e-11 9.88816e-11 2 1.068087340161182e+00 1.068087340182548e+00 2.13658e-11 6.93043e-09 * 3 2.160129434054004e+00 2.160129433947227e+00 1.06777e-10 9.08698e-10 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -1.642640580026348e-02 -1.642640582496397e-02 2.47005e-11 6.19194e-10 2 6.019361646500215e-01 6.019361646229405e-01 2.70810e-11 1.95309e-10 3 5.147909137684292e-02 5.147909144036780e-02 6.35249e-11 1.72148e-10 ----------------------------------------------------------------------------------------------------- 18 Cu 1 -2.232577000557724e-01 -2.232576999460200e-01 1.09752e-10 1.52878e-09 2 9.754384522945596e-01 9.754384523596619e-01 6.51023e-11 3.32760e-09 * 3 6.753004005475791e-01 6.753004008361381e-01 2.88559e-10 2.13520e-09 ----------------------------------------------------------------------------------------------------- 19 Cu 1 1.957911107768749e-01 1.957911107896039e-01 1.27290e-11 1.90543e-10 2 1.339735476465263e-02 1.339735478986803e-02 2.52154e-11 3.45462e-10 3 3.753711144805477e-01 3.753711144548643e-01 2.56835e-11 5.48013e-11 ----------------------------------------------------------------------------------------------------- 20 Cu 1 7.837109773831140e-01 7.837109773847978e-01 1.68376e-12 9.69830e-11 2 -1.265946430687837e-01 -1.265946432536937e-01 1.84910e-10 1.98191e-09 3 -8.192146058621830e-01 -8.192146058584564e-01 3.72657e-12 2.19907e-10 ----------------------------------------------------------------------------------------------------- 21 Al 1 -3.417753681892498e+00 -3.417753681903756e+00 1.12577e-11 6.04660e-10 2 -5.008549632318439e-01 -5.008549631008542e-01 1.30990e-10 6.43286e-08 * 3 -4.021239147389596e-01 -4.021239148840564e-01 1.45097e-10 1.95229e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 -4.700063059639928e-01 -4.700063059724697e-01 8.47689e-12 4.55346e-10 2 -8.996162971520301e-01 -8.996162971672423e-01 1.52123e-11 1.29024e-10 3 -1.242763837971531e+00 -1.242763837911292e+00 6.02394e-11 1.07303e-09 ----------------------------------------------------------------------------------------------------- 23 Al 1 1.650680712272227e+00 1.650680712287748e+00 1.55214e-11 2.82860e-10 2 6.549878046231068e-01 6.549878046237828e-01 6.76015e-13 1.86135e-10 3 1.373267442675216e+00 1.373267442676281e+00 1.06470e-12 2.67053e-10 ----------------------------------------------------------------------------------------------------- 24 Cu 1 -2.991637300717526e+00 -2.991637300729129e+00 1.16027e-11 5.09552e-10 2 -2.421222509570972e+00 -2.421222509533631e+00 3.73412e-11 3.35251e-10 3 -1.010526313579413e-01 -1.010526313803968e-01 2.24556e-11 7.44158e-11 ----------------------------------------------------------------------------------------------------- 25 Al 1 -2.350578159494303e+00 -2.350578159478767e+00 1.55365e-11 3.20633e-10 2 -1.638572239105894e+00 -1.638572239106355e+00 4.60521e-13 4.64921e-11 3 -8.928784594276730e-01 -8.928784593664042e-01 6.12688e-11 2.63569e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 7.403935246608447e-01 7.403935247202481e-01 5.94034e-11 1.31067e-09 2 5.181625584307066e+00 5.181625584258946e+00 4.81206e-11 2.66844e-10 3 -3.001777541245491e+00 -3.001777541258482e+00 1.29909e-11 1.11006e-09 ----------------------------------------------------------------------------------------------------- 27 Al 1 3.850767219676432e-01 3.850767219699615e-01 2.31826e-12 2.14207e-08 * 2 -6.479409340165438e+00 -6.479409340165869e+00 4.31655e-13 2.86026e-08 * 3 4.076263969245240e+00 4.076263969251452e+00 6.21192e-12 1.45624e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -3.046731525232465e+00 -3.046731525235491e+00 3.02602e-12 4.90679e-10 2 2.073789812720182e+00 2.073789813484989e+00 7.64807e-10 1.03673e-08 * 3 1.787087470104366e+00 1.787087469963518e+00 1.40847e-10 5.08667e-10 ----------------------------------------------------------------------------------------------------- 29 Cu 1 2.870016630844180e+00 2.870016630788143e+00 5.60370e-11 4.09168e-10 2 -1.347066069547208e+00 -1.347066069497242e+00 4.99663e-11 3.93128e-09 * 3 -2.913971595859902e+00 -2.913971595876439e+00 1.65370e-11 1.37686e-09 ----------------------------------------------------------------------------------------------------- 30 Al 1 -2.474308601831916e-01 -2.474308601951220e-01 1.19305e-11 2.18565e-10 2 -5.822598658198263e-01 -5.822598657991396e-01 2.06867e-11 2.34111e-10 3 -2.198233775684752e-02 -2.198233780193086e-02 4.50833e-11 1.82043e-10 ----------------------------------------------------------------------------------------------------- 31 Al 1 2.350780030481225e+00 2.350780030457388e+00 2.38378e-11 4.22872e-10 2 2.928570512694143e+00 2.928570512810438e+00 1.16295e-10 1.24486e-09 3 1.329796743088327e+00 1.329796743076936e+00 1.13904e-11 1.30959e-08 * ----------------------------------------------------------------------------------------------------- 32 Al 1 1.993090237756879e+00 1.993090237888147e+00 1.31268e-10 4.64557e-11 2 2.161111944349794e+00 2.161111944333908e+00 1.58868e-11 1.92851e-10 3 1.158041320566161e+00 1.158041320575910e+00 9.74931e-12 4.69509e-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 dicontinuities. Maximum error obtained for particle = 30, direction = 3: |F_model - F_numer| error = ----------------------- = 2.05089e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.03346e-08 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: B Comment: The letter grade B was assigned because the normalized error in the computation was 1.03346e-08 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.