!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Tersoff_LAMMPS_Erhart_Albe_CSi__MO_903987585848_001 Supported species : C Si 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 = 2.73904800415 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 -4.947526179025463e+00 -4.947526179025306e+00 1.57208e-13 4.79838e-11 2 -6.402262271809109e+00 -6.402262271814942e+00 5.83356e-12 1.60529e-11 3 -1.298629920092189e+00 -1.298629920090616e+00 1.57319e-12 7.02816e-12 ----------------------------------------------------------------------------------------------------- 2 C 1 6.553124115452778e+00 6.553124115442541e+00 1.02371e-11 4.74714e-11 2 8.043827233791493e+00 8.043827233785890e+00 5.60263e-12 6.26166e-11 3 -1.308357191682495e+00 -1.308357191681627e+00 8.68194e-13 4.71432e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 1.428737411906275e+00 1.428737411909510e+00 3.23519e-12 5.22911e-11 2 -3.357475848012005e+00 -3.357475848009156e+00 2.84928e-12 6.32472e-12 3 -1.994274156273538e-01 -1.994274156308543e-01 3.50045e-12 3.16459e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 -4.478653910427631e+00 -4.478653910423248e+00 4.38227e-12 3.59668e-11 2 7.335193267907522e+00 7.335193267897602e+00 9.92006e-12 1.01942e-10 3 -2.693548269297835e+00 -2.693548269295117e+00 2.71783e-12 9.50870e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 5.076190896629058e+00 5.076190896629427e+00 3.69482e-13 2.27027e-11 2 -5.250595551110059e+00 -5.250595551111251e+00 1.19282e-12 5.45910e-11 3 1.896412120995130e+00 1.896412120998140e+00 3.00937e-12 4.04468e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -4.007364525087826e+00 -4.007364525056421e+00 3.14051e-11 3.45204e-10 * 2 2.033089171229947e+00 2.033089171214448e+00 1.54992e-11 3.34479e-11 3 -7.932597162919578e-01 -7.932597163039137e-01 1.19559e-11 8.55246e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 -7.094886925133749e+00 -7.094886925123447e+00 1.03020e-11 5.33920e-11 2 -7.492533460086262e+00 -7.492533460077436e+00 8.82672e-12 7.03304e-11 3 -1.582988581399490e+01 -1.582988581399188e+01 3.02336e-12 5.31344e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 -6.837144515674817e-01 -6.837144515538989e-01 1.35828e-11 1.60754e-10 2 -1.086502154676646e+00 -1.086502154688382e+00 1.17368e-11 3.65104e-11 3 -6.163151417377574e-01 -6.163151417314063e-01 6.35103e-12 5.33411e-11 ----------------------------------------------------------------------------------------------------- 9 C 1 -5.284194595604147e+00 -5.284194595585370e+00 1.87770e-11 2.55314e-10 2 -5.532814530214033e-01 -5.532814530157560e-01 5.64726e-12 3.13763e-11 3 -1.942603678244733e+00 -1.942603678253867e+00 9.13425e-12 1.88876e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 -1.224184188058615e+01 -1.224184188058675e+01 6.03961e-13 4.94911e-11 2 3.579733532522002e+00 3.579733532523364e+00 1.36202e-12 1.20442e-10 3 -2.226919377921290e+01 -2.226919377921112e+01 1.78346e-12 5.83924e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 5.469303067743089e+00 5.469303067734224e+00 8.86580e-12 1.75522e-11 2 -8.990396444121542e-01 -8.990396444068303e-01 5.32396e-12 8.96372e-11 3 1.368595645959930e+00 1.368595645925757e+00 3.41731e-11 5.35636e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 -8.111104001823320e-01 -8.111104001853635e-01 3.03146e-12 4.42357e-11 2 -7.957756984862344e-01 -7.957756984858505e-01 3.83915e-13 4.50484e-12 3 -1.752488185444783e+00 -1.752488185438327e+00 6.45595e-12 4.11329e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 3.747868307197735e+00 3.747868307200110e+00 2.37499e-12 8.48428e-11 2 -8.914605981702984e+00 -8.914605981696567e+00 6.41620e-12 1.10546e-10 3 -7.958886881370560e+00 -7.958886881367923e+00 2.63700e-12 3.51772e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 -1.463258988986412e-01 -1.463258989004551e-01 1.81385e-12 1.21151e-10 2 -7.859822235981703e-01 -7.859822235891851e-01 8.98515e-12 5.06019e-11 3 -1.835333317091526e-01 -1.835333317102638e-01 1.11122e-12 3.03106e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 6.540871307967829e+00 6.540871307951756e+00 1.60734e-11 9.36851e-11 2 6.055377360497631e+00 6.055377360508860e+00 1.12292e-11 2.13015e-10 3 5.999234679583448e+00 5.999234679572377e+00 1.10711e-11 3.87388e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 1.459996189651546e+01 1.459996189649717e+01 1.82965e-11 5.59961e-11 2 4.530300118891666e+00 4.530300118890870e+00 7.95808e-13 3.09122e-11 3 1.985885955113660e+01 1.985885955112946e+01 7.14095e-12 4.05862e-11 ----------------------------------------------------------------------------------------------------- 17 C 1 1.916910959667064e+00 1.916910959668219e+00 1.15574e-12 3.09648e-11 2 4.997829140680582e-01 4.997829140664785e-01 1.57979e-12 9.43445e-12 3 9.662500120284101e-02 9.662500120513244e-02 2.29143e-12 3.80419e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 1.446068940186850e+00 1.446068940228626e+00 4.17757e-11 3.52907e-11 2 -2.324585354029451e+00 -2.324585354048200e+00 1.87490e-11 4.99671e-11 3 4.887100042985935e-01 4.887100042608928e-01 3.77007e-11 1.21361e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 4.406377709558389e+00 4.406377709579795e+00 2.14060e-11 6.42544e-11 2 4.760674895608452e+00 4.760674895601145e+00 7.30704e-12 4.65397e-11 3 -4.792719733604763e-01 -4.792719733642491e-01 3.77276e-12 5.03923e-10 * ----------------------------------------------------------------------------------------------------- 20 C 1 1.236654421711194e-01 1.236654421777143e-01 6.59496e-12 3.55192e-11 2 -1.057730607473395e+00 -1.057730607481835e+00 8.44014e-12 1.18316e-11 3 1.746792944493886e+00 1.746792944479954e+00 1.39317e-11 1.44054e-11 ----------------------------------------------------------------------------------------------------- 21 C 1 -9.969271961613931e+00 -9.969271961596355e+00 1.75753e-11 2.58265e-11 2 -4.577110487071906e+00 -4.577110487073593e+00 1.68754e-12 1.45180e-10 3 3.364251329611071e+00 3.364251329640256e+00 2.91851e-11 6.92606e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 9.514935895648883e+00 9.514935895647611e+00 1.27187e-12 1.30580e-10 2 1.211431366727883e+01 1.211431366727647e+01 2.35190e-12 1.30651e-10 3 9.352155156989390e+00 9.352155156991111e+00 1.72129e-12 6.91358e-12 ----------------------------------------------------------------------------------------------------- 23 C 1 1.323999132165000e+00 1.323999132170169e+00 5.16875e-12 1.06870e-11 2 4.770500211259987e-01 4.770500211206834e-01 5.31530e-12 1.31066e-11 3 1.114363565802841e+00 1.114363565799128e+00 3.71347e-12 2.68257e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 -6.553733994055317e-01 -6.553733993964198e-01 9.11193e-12 4.98452e-11 2 -7.749365894128528e-01 -7.749365894082108e-01 4.64206e-12 1.50140e-10 3 -4.903701374954537e-02 -4.903701373251383e-02 1.70315e-11 7.01692e-11 ----------------------------------------------------------------------------------------------------- 25 C 1 -1.082375955005647e+01 -1.082375955005633e+01 1.38556e-13 6.35829e-11 2 -6.055882987179887e+00 -6.055882987179577e+00 3.09974e-13 9.09504e-11 3 -4.619153239732823e-01 -4.619153239655685e-01 7.71377e-12 5.16852e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 2.254420034974304e+00 2.254420034980512e+00 6.20837e-12 1.35043e-10 2 5.521421873058032e+00 5.521421873060249e+00 2.21689e-12 1.79223e-10 3 -4.667269518241985e+00 -4.667269518238707e+00 3.27827e-12 8.00275e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 2.444831255043459e+01 2.444831255044445e+01 9.85168e-12 1.84777e-11 2 -2.990362251031448e+01 -2.990362251030614e+01 8.33822e-12 4.98090e-12 3 1.490565258442234e+01 1.490565258443113e+01 8.79119e-12 1.15206e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 -3.203717086516242e+01 -3.203717086517877e+01 1.63496e-11 4.31157e-11 2 2.910520676807611e+01 2.910520676809219e+01 1.60831e-11 9.60689e-11 3 -2.243726129453708e+00 -2.243726129455148e+00 1.43974e-12 5.65195e-10 * ----------------------------------------------------------------------------------------------------- 29 C 1 -2.504506705811213e+00 -2.504506705818510e+00 7.29727e-12 1.61693e-10 2 -3.034369124676053e-01 -3.034369124384546e-01 2.91508e-11 1.17149e-06 * 3 3.920113051660449e+00 3.920113051627884e+00 3.25655e-11 9.56879e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 4.116416008022717e+00 4.116416008010102e+00 1.26148e-11 6.77289e-11 2 5.670258937808561e-01 5.670258937753245e-01 5.53158e-12 3.70127e-11 3 -2.980669204105333e+00 -2.980669204095919e+00 9.41380e-12 6.14260e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 -2.004529471628740e+00 -2.004529471629878e+00 1.13776e-12 3.24709e-11 2 -5.103859544989860e+00 -5.103859545000080e+00 1.02194e-11 4.14220e-11 3 1.532514433425008e+00 1.532514433432567e+00 7.55884e-12 2.46525e-10 ----------------------------------------------------------------------------------------------------- 32 C 1 4.723067043950580e+00 4.723067043919762e+00 3.08180e-11 2.98455e-10 * 2 1.016222562017880e+00 1.016222562017114e+00 7.66054e-13 2.55173e-10 3 2.083738418009407e+00 2.083738417977404e+00 3.20024e-11 8.90607e-05 * ----------------------------------------------------------------------------------------------------- * 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 = 24, direction = 3: |F_model - F_numer| error = --------------------------------- = 3.47320e-10 max{(|F_model|+|F_numer|)/2, 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 = Si | a0 = 3.84633159637 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 1.486348647098229e+00 1.486348647098657e+00 4.28102e-13 3.46534e-11 2 1.851250541443889e+00 1.851250541444742e+00 8.53317e-13 3.14335e-11 3 7.918646275908566e-01 7.918646275893447e-01 1.51190e-12 4.44934e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 1.022172066959787e+00 1.022172066959092e+00 6.94333e-13 1.16556e-11 2 -5.888479871613833e+00 -5.888479871613275e+00 5.57776e-13 3.42872e-11 3 2.410430342539752e+00 2.410430342538376e+00 1.37534e-12 4.68030e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 2.850743655695695e+00 2.850743655686454e+00 9.24016e-12 3.83960e-11 2 1.822331029218337e+00 1.822331029222012e+00 3.67484e-12 5.78784e-11 3 8.377191227553022e-01 8.377191227698493e-01 1.45470e-11 4.73510e-12 ----------------------------------------------------------------------------------------------------- 4 Si 1 8.602730530005152e-01 8.602730530022625e-01 1.74738e-12 6.59073e-12 2 -3.393610293268702e+00 -3.393610293262906e+00 5.79625e-12 5.73825e-11 3 -4.257842259852692e-01 -4.257842259849388e-01 3.30458e-13 8.25190e-12 ----------------------------------------------------------------------------------------------------- 5 Si 1 -2.538535343758065e+00 -2.538535343758030e+00 3.55271e-14 1.37454e-11 2 7.465897688190661e+00 7.465897688189059e+00 1.60227e-12 4.25864e-11 3 3.406745243494135e+00 3.406745243501354e+00 7.21823e-12 9.10072e-12 ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.595566766922827e+00 -2.595566766912916e+00 9.91118e-12 7.03508e-11 2 -2.793377366790020e+00 -2.793377366784509e+00 5.51115e-12 3.00195e-11 3 -2.408799817669092e-02 -2.408799817492047e-02 1.77044e-12 3.54652e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -7.737363376202127e-01 -7.737363376175875e-01 2.62512e-12 5.59371e-11 2 6.086509176964743e-01 6.086509176980792e-01 1.60494e-12 3.08241e-11 3 -1.826754537255329e-01 -1.826754537178423e-01 7.69065e-12 1.74421e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -9.946441789682607e-01 -9.946441789849362e-01 1.66754e-11 9.13680e-12 2 -1.331688635979311e+00 -1.331688635959980e+00 1.93312e-11 4.26064e-10 * 3 5.618300892824354e-01 5.618300892932652e-01 1.08298e-11 2.44352e-11 ----------------------------------------------------------------------------------------------------- 9 Si 1 -3.834929019994634e+00 -3.834929019995052e+00 4.17888e-13 6.95399e-12 2 -3.850263477709730e+00 -3.850263477708971e+00 7.58060e-13 5.22382e-12 3 -1.834125354370018e+00 -1.834125354364808e+00 5.20983e-12 1.04963e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 7.517052640715602e+00 7.517052640726713e+00 1.11111e-11 1.17364e-11 2 3.591758786356485e+00 3.591758786355721e+00 7.64722e-13 2.73959e-11 3 -9.339894588729667e-01 -9.339894588748223e-01 1.85563e-12 1.97884e-10 * ----------------------------------------------------------------------------------------------------- 11 Si 1 2.521715803730730e+00 2.521715803688168e+00 4.25620e-11 1.77761e-10 * 2 -1.029940976001147e+00 -1.029940976015641e+00 1.44937e-11 2.86932e-10 * 3 -2.830918223794497e-01 -2.830918223658060e-01 1.36436e-11 3.24883e-10 * ----------------------------------------------------------------------------------------------------- 12 Si 1 -1.862249239640202e+00 -1.862249239645995e+00 5.79314e-12 1.85056e-11 2 7.485726475896470e-01 7.485726475878769e-01 1.77014e-12 2.05538e-11 3 1.675597718726316e+00 1.675597718730089e+00 3.77320e-12 1.28384e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -2.071003089049479e+00 -2.071003089043590e+00 5.88951e-12 2.18754e-11 2 3.310966379635479e+00 3.310966379639713e+00 4.23395e-12 1.32623e-11 3 1.113263567943418e+00 1.113263567955264e+00 1.18463e-11 1.91283e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 -5.925355709104614e-01 -5.925355709082764e-01 2.18503e-12 5.35442e-10 * 2 -3.701703113829752e+00 -3.701703113833949e+00 4.19709e-12 2.42126e-11 3 3.880045158102758e+00 3.880045158108008e+00 5.25047e-12 1.48668e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 -3.891881141591068e-01 -3.891881141729469e-01 1.38400e-11 1.88523e-11 2 -6.732348165668768e-01 -6.732348165324551e-01 3.44217e-11 5.65996e-11 3 -8.600391609063138e+00 -8.600391609063642e+00 5.04485e-13 2.22862e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 2.414790011887350e-01 2.414790011829714e-01 5.76358e-12 1.60382e-10 2 1.783630793357947e+00 1.783630793364932e+00 6.98530e-12 9.69784e-11 3 -5.863457808711961e+00 -5.863457808708117e+00 3.84404e-12 4.95026e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 1.901290597171903e+00 1.901290597171833e+00 7.01661e-14 1.03717e-11 2 1.109560293379400e+00 1.109560293364146e+00 1.52538e-11 3.50202e-11 3 -2.360516533477073e+00 -2.360516533473006e+00 4.06697e-12 1.21902e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 -1.749574679558221e+00 -1.749574679555833e+00 2.38765e-12 5.10856e-11 2 -2.058584359024671e+00 -2.058584359047733e+00 2.30620e-11 1.72355e-11 3 -2.650327837123654e+00 -2.650327837118655e+00 4.99911e-12 1.07740e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 -5.326121007788653e+00 -5.326121007792590e+00 3.93729e-12 6.64357e-12 2 4.406752004249271e+00 4.406752004247545e+00 1.72662e-12 2.39488e-11 3 1.323924600174548e+00 1.323924600174513e+00 3.50830e-14 2.69704e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 3.045776733406088e+00 3.045776733403892e+00 2.19647e-12 2.88587e-11 2 -3.502096273591773e+00 -3.502096273575277e+00 1.64957e-11 2.46297e-10 * 3 -1.894221703018504e+00 -1.894221703019571e+00 1.06692e-12 1.17051e-10 ----------------------------------------------------------------------------------------------------- 21 Si 1 3.015480439366648e+00 3.015480439364382e+00 2.26619e-12 8.40954e-11 2 -4.111760974543148e+00 -4.111760974519264e+00 2.38840e-11 3.49765e-11 3 -5.495375279707076e+00 -5.495375279708461e+00 1.38467e-12 2.24798e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 -1.313839411972448e+00 -1.313839411974498e+00 2.05036e-12 3.93239e-11 2 6.666588068736987e-02 6.666588068811162e-02 7.41754e-13 4.23543e-11 3 7.484564659428310e+00 7.484564659424560e+00 3.74989e-12 4.85221e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -3.142216057887557e+00 -3.142216057897634e+00 1.00768e-11 1.39240e-11 2 3.034250242685161e+00 3.034250242683434e+00 1.72662e-12 4.29012e-11 3 -5.942299856180057e+00 -5.942299856169523e+00 1.05338e-11 2.53060e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 4.915619114015752e+00 4.915619114019587e+00 3.83515e-12 1.91321e-10 * 2 5.759198569608973e+00 5.759198569598398e+00 1.05747e-11 3.72449e-11 3 3.321856794863482e+00 3.321856794865377e+00 1.89448e-12 3.73004e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 8.293268597727954e-01 8.293268597744295e-01 1.63414e-12 2.52352e-10 * 2 1.934336236591268e+00 1.934336236582359e+00 8.90843e-12 2.72398e-11 3 4.899777085770641e+00 4.899777085760910e+00 9.73088e-12 3.71090e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 -8.062848820448078e+00 -8.062848820443064e+00 5.01466e-12 5.56692e-11 2 3.616562219937399e+00 3.616562219944990e+00 7.59037e-12 5.62896e-11 3 3.025117067444433e+00 3.025117067461146e+00 1.67129e-11 7.15481e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 -1.648144969771860e+00 -1.648144969779516e+00 7.65565e-12 9.58049e-11 2 4.643999438258717e+00 4.643999438267515e+00 8.79741e-12 2.63318e-11 3 2.617292161407832e+00 2.617292161406841e+00 9.91651e-13 1.43885e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 4.631738164034013e+00 4.631738164035053e+00 1.03917e-12 3.34426e-11 2 -4.987974264439364e+00 -4.987974264444945e+00 5.58131e-12 6.86935e-11 3 -6.601662398564324e+00 -6.601662398586009e+00 2.16849e-11 2.67795e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 2.310725060286382e+00 2.310725060307258e+00 2.08757e-11 9.97784e-11 2 -8.921343036843245e+00 -8.921343036847748e+00 4.50306e-12 3.62768e-11 3 2.362129476708947e-01 2.362129476774587e-01 6.56394e-12 1.44456e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 4.557571804975737e-01 4.557571804862866e-01 1.12871e-11 1.18867e-10 2 4.218865795580487e+00 4.218865795600800e+00 2.03135e-11 5.27987e-11 3 5.129687975965883e+00 5.129687975963188e+00 2.69473e-12 1.02164e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 -2.550167893732925e+00 -2.550167893733773e+00 8.47766e-13 1.53881e-10 2 -5.450032721307649e+00 -5.450032721311193e+00 3.54383e-12 5.46425e-11 3 -3.513124465665756e+00 -3.513124465651814e+00 1.39422e-11 5.83031e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 1.839801485242546e+00 1.839801485240248e+00 2.29794e-12 1.21893e-10 2 1.720840717042252e+00 1.720840717043569e+00 1.31650e-12 5.22316e-12 3 3.889202641860481e+00 3.889202641860503e+00 2.13163e-14 5.26779e-11 ----------------------------------------------------------------------------------------------------- * 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 = 6, direction = 3: |F_model - F_numer| error = --------------------------------- = 7.34990e-11 max{(|F_model|+|F_numer|)/2, 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 Si | a0 = 3.24853923932 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 2.785329530298111e+00 2.785329529782452e+00 5.15660e-10 3.53607e-09 2 -1.317998089257149e+00 -1.317998089154096e+00 1.03052e-10 4.47070e-10 3 4.945505635090675e-01 4.945505633284074e-01 1.80660e-10 4.02743e-09 ----------------------------------------------------------------------------------------------------- 2 Si 1 -6.016782043606133e+00 -6.016782043690870e+00 8.47367e-11 1.11077e-08 2 -8.797520324734162e+00 -8.797520324714757e+00 1.94049e-11 3.99718e-09 3 -5.619728767806051e+00 -5.619728768079210e+00 2.73159e-10 1.04826e-08 ----------------------------------------------------------------------------------------------------- 3 C 1 -2.868929099727862e+00 -2.868929099691009e+00 3.68527e-11 4.27419e-10 2 9.784969626122969e-01 9.784969626034146e-01 8.88234e-12 7.34299e-10 3 -2.785924578356592e+00 -2.785924578386772e+00 3.01803e-11 1.23604e-09 ----------------------------------------------------------------------------------------------------- 4 Si 1 -5.806168286115180e+00 -5.806168286200013e+00 8.48335e-11 4.33470e-09 2 -5.542769323588646e+00 -5.542769327798358e+00 4.20971e-09 7.56832e-09 3 -3.371372125446907e+00 -3.371372128186105e+00 2.73920e-09 2.83488e-08 ----------------------------------------------------------------------------------------------------- 5 C 1 -5.417076045071451e+00 -5.417076044214674e+00 8.56777e-10 3.23186e-09 2 -1.846191910718129e+00 -1.846191911661906e+00 9.43778e-10 1.70674e-09 3 -7.777024763072929e+00 -7.777024763278831e+00 2.05902e-10 1.13817e-08 ----------------------------------------------------------------------------------------------------- 6 Si 1 3.588978802363143e+00 3.588978802255560e+00 1.07583e-10 5.60759e-10 2 -2.569889856724402e+00 -2.569889857855706e+00 1.13130e-09 3.08445e-09 3 -2.945502939844969e+00 -2.945502940737723e+00 8.92754e-10 1.00742e-08 ----------------------------------------------------------------------------------------------------- 7 C 1 9.115529776838430e+00 9.115529775360214e+00 1.47822e-09 2.54715e-08 2 -1.203428924516975e+00 -1.203428924729434e+00 2.12459e-10 3.07122e-09 3 1.120235621877646e+01 1.120235621940985e+01 6.33394e-10 1.90341e-08 ----------------------------------------------------------------------------------------------------- 8 C 1 -1.347084624440718e+00 -1.347084623016394e+00 1.42432e-09 5.04732e-09 2 7.540266258697672e-01 7.540266262679728e-01 3.98206e-10 2.43946e-09 3 5.574075052706811e+00 5.574075052788131e+00 8.13198e-11 1.62363e-09 ----------------------------------------------------------------------------------------------------- 9 C 1 2.627697781544394e-01 2.627697750647261e-01 3.08971e-09 1.24941e-08 2 -2.848821399280773e-01 -2.848821417098951e-01 1.78182e-09 5.20095e-09 3 1.109723014556808e+00 1.109723015482462e+00 9.25654e-10 2.31697e-08 ----------------------------------------------------------------------------------------------------- 10 Si 1 -3.368865588437263e+00 -3.368865589589329e+00 1.15207e-09 2.70683e-09 2 3.344206073211629e+00 3.344206073148872e+00 6.27574e-11 9.48857e-10 3 1.165167646794994e+00 1.165167647582726e+00 7.87732e-10 9.80015e-10 ----------------------------------------------------------------------------------------------------- 11 Si 1 -2.468372890446462e+00 -2.468372891274608e+00 8.28146e-10 6.52399e-08 * 2 1.082642083366506e+01 1.082642083304789e+01 6.17167e-10 3.77053e-09 3 7.420870204057403e+00 7.420870204233547e+00 1.76144e-10 3.73768e-09 ----------------------------------------------------------------------------------------------------- 12 C 1 2.784631010169656e+00 2.784631010146405e+00 2.32507e-11 7.33588e-10 2 -9.662120941088702e-01 -9.662120940082297e-01 1.00640e-10 2.82327e-09 3 -1.051364877442958e+00 -1.051364877463565e+00 2.06077e-11 5.70221e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 6.333106949018546e+00 6.333106948889501e+00 1.29045e-10 5.64463e-09 2 5.487798955373923e+00 5.487798955265672e+00 1.08251e-10 1.12089e-09 3 -8.040289454784141e+00 -8.040289455639837e+00 8.55696e-10 3.94524e-09 ----------------------------------------------------------------------------------------------------- 14 C 1 -6.606283068375482e-02 -6.606282905226346e-02 1.63149e-09 3.21583e-09 2 4.106752800851948e-02 4.106752791192507e-02 9.65944e-11 4.65958e-10 3 -3.143451203726101e-01 -3.143451208748573e-01 5.02247e-10 3.55844e-09 ----------------------------------------------------------------------------------------------------- 15 C 1 7.390711079952043e-01 7.390711072674213e-01 7.27783e-10 1.90718e-08 2 -2.885421352751234e+00 -2.885421350723197e+00 2.02804e-09 2.52754e-08 3 1.937302436083137e+00 1.937302436147966e+00 6.48293e-11 1.12458e-08 ----------------------------------------------------------------------------------------------------- 16 C 1 -3.545499143210324e+00 -3.545499143183669e+00 2.66542e-11 3.70277e-09 2 -1.555484695874664e+00 -1.555484697574127e+00 1.69946e-09 9.88591e-09 3 -2.937198867682087e+00 -2.937198868283690e+00 6.01603e-10 5.67158e-09 ----------------------------------------------------------------------------------------------------- 17 C 1 -7.967264597165910e+00 -7.967264595364565e+00 1.80134e-09 6.05533e-09 2 -9.158583907357267e+00 -9.158583904875634e+00 2.48163e-09 5.65327e-09 3 -8.310845793509264e-01 -8.310845788726429e-01 4.78284e-10 8.95522e-09 ----------------------------------------------------------------------------------------------------- 18 C 1 1.277853054464676e+01 1.277853054823282e+01 3.58606e-09 1.12190e-08 2 8.302692162672477e+00 8.302692164238428e+00 1.56595e-09 1.39096e-08 3 -6.771328505879900e-01 -6.771328536205298e-01 3.03254e-09 3.29271e-08 * ----------------------------------------------------------------------------------------------------- 19 Si 1 4.967214831352219e+00 4.967214831718745e+00 3.66525e-10 9.07988e-10 2 -9.156711520128013e+00 -9.156711520300384e+00 1.72371e-10 5.50008e-09 3 -1.786495745921199e+00 -1.786495745128840e+00 7.92359e-10 3.87834e-08 * ----------------------------------------------------------------------------------------------------- 20 Si 1 -1.152807096091882e+01 -1.152807096077395e+01 1.44878e-10 3.31510e-09 2 6.453212506226877e+00 6.453212504878205e+00 1.34867e-09 6.02361e-09 3 5.785816527354370e+00 5.785816527617993e+00 2.63623e-10 4.77214e-09 ----------------------------------------------------------------------------------------------------- 21 C 1 8.738502718078133e-01 8.738502697118696e-01 2.09594e-09 2.24571e-08 2 -1.214030691510445e+00 -1.214030691249213e+00 2.61232e-10 1.74755e-09 3 1.995420198113503e+00 1.995420199818432e+00 1.70493e-09 5.98947e-09 ----------------------------------------------------------------------------------------------------- 22 Si 1 5.183925736308440e-01 5.183925736452614e-01 1.44174e-11 5.52377e-09 2 -2.313727128555653e+00 -2.313727128241574e+00 3.14079e-10 1.48607e-09 3 -1.532265303654080e+01 -1.532265303538546e+01 1.15534e-09 1.13218e-07 * ----------------------------------------------------------------------------------------------------- 23 C 1 7.664683561623886e-02 7.664683626435526e-02 6.48116e-10 1.11866e-07 * 2 -3.693316960512188e+00 -3.693316960462299e+00 4.98894e-11 5.33462e-09 3 -1.054921965619014e+00 -1.054921960292194e+00 5.32682e-09 3.11288e-08 ----------------------------------------------------------------------------------------------------- 24 Si 1 -2.356239963639284e+00 -2.356239963394102e+00 2.45182e-10 2.39237e-09 2 2.799169271216990e+00 2.799169271074762e+00 1.42228e-10 3.64328e-10 3 3.690173557194182e+00 3.690173557650975e+00 4.56793e-10 1.18858e-09 ----------------------------------------------------------------------------------------------------- 25 C 1 2.050999321027071e-01 2.050999328120618e-01 7.09355e-10 6.65736e-10 2 2.604004377881429e+00 2.604004376094319e+00 1.78711e-09 3.86576e-09 3 2.934745227638112e+00 2.934745229503803e+00 1.86569e-09 3.30442e-09 ----------------------------------------------------------------------------------------------------- 26 C 1 -1.009222244904756e+00 -1.009222244803567e+00 1.01189e-10 1.37513e-08 2 4.001150982937767e-01 4.001150955804710e-01 2.71331e-09 3.40237e-09 3 7.955726654402887e-01 7.955726649460668e-01 4.94222e-10 2.13164e-09 ----------------------------------------------------------------------------------------------------- 27 Si 1 1.477751698196649e+01 1.477751698173897e+01 2.27519e-10 2.70918e-09 2 -1.388628107232367e+01 -1.388628107196731e+01 3.56367e-10 2.56264e-08 3 3.300371944527935e+00 3.300371946649539e+00 2.12160e-09 1.28093e-08 ----------------------------------------------------------------------------------------------------- 28 Si 1 -1.558783072140283e+01 -1.558783072162842e+01 2.25585e-10 6.24899e-09 2 1.327106909318116e+01 1.327106909333728e+01 1.56119e-10 6.62489e-09 3 -3.974189457924453e+00 -3.974189458594330e+00 6.69877e-10 3.23186e-09 ----------------------------------------------------------------------------------------------------- 29 C 1 1.320066736092472e-01 1.320066737081964e-01 9.89493e-11 7.90507e-09 2 -1.023091247055652e+00 -1.023091247446356e+00 3.90703e-10 6.87379e-09 3 -2.518946156241613e+00 -2.518946156040277e+00 2.01336e-10 4.40892e-09 ----------------------------------------------------------------------------------------------------- 30 Si 1 7.017578302110044e+00 7.017578302377526e+00 2.67482e-10 2.12652e-09 2 4.128214449855770e+00 4.128214449746221e+00 1.09549e-10 4.66351e-09 3 7.532519345758607e+00 7.532519348552154e+00 2.79355e-09 2.77065e-09 ----------------------------------------------------------------------------------------------------- 31 Si 1 2.004321700990472e-01 2.004321703815292e-01 2.82482e-10 2.87120e-09 2 7.093652195585324e+00 7.093652196178073e+00 5.92750e-10 6.38525e-09 3 6.276876252574185e+00 6.276876252801813e+00 2.27628e-10 1.52383e-09 ----------------------------------------------------------------------------------------------------- 32 Si 1 2.196782967991803e+00 2.196782969134705e+00 1.14290e-09 1.88804e-09 2 9.313951059902051e-01 9.313951054304038e-01 5.59801e-10 2.39059e-09 3 -2.073655680906361e-01 -2.073655684476957e-01 3.57060e-10 2.18746e-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 dicontinuities. Maximum error obtained for particle = 14, direction = 1: |F_model - F_numer| error = --------------------------------- = 2.46961e-08 max{(|F_model|+|F_numer|)/2, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.46961e-08 Machine precision = 2.22045e-16 Grade: B Comment: The letter grade B was assigned because the normalized error in the computation was 2.46961e-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. 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.