!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Tersoff_1989_SiGe__MO_350526375143_004 Supported species : Ge 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 = Ge | a0 = 4.023588180541992 | (Configuration in file "config-Ge.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ge 1 6.060735949465058e+00 6.060735949464217e+00 8.41105e-13 5.46274e-11 2 3.041304174181283e+00 3.041304174180520e+00 7.62945e-13 1.71272e-11 3 1.987445885979092e+00 1.987445885971862e+00 7.22999e-12 8.90272e-11 ----------------------------------------------------------------------------------------------------- 2 Ge 1 -4.059738781400134e+00 -4.059738781400325e+00 1.90958e-13 1.38510e-10 2 5.018433045807429e-01 5.018433045827738e-01 2.03093e-12 3.29669e-11 3 3.037905524703527e+00 3.037905524689637e+00 1.38898e-11 2.24953e-11 ----------------------------------------------------------------------------------------------------- 3 Ge 1 -1.078366292286802e+00 -1.078366292287517e+00 7.15428e-13 1.05069e-09 * 2 5.231383323832909e-01 5.231383323762545e-01 7.03637e-12 1.24649e-10 3 -3.884089201701975e+00 -3.884089201687208e+00 1.47669e-11 7.33373e-11 ----------------------------------------------------------------------------------------------------- 4 Ge 1 4.467527525378215e+00 4.467527525380077e+00 1.86162e-12 1.38598e-10 2 4.814230425684749e+00 4.814230425683315e+00 1.43352e-12 1.30803e-10 3 1.975741975728411e+00 1.975741975728976e+00 5.64215e-13 1.58904e-11 ----------------------------------------------------------------------------------------------------- 5 Ge 1 -3.874214365923032e-01 -3.874214365937936e-01 1.49042e-12 2.04153e-10 2 6.156722907621346e-01 6.156722907574416e-01 4.69302e-12 2.70585e-11 3 2.134666091080236e+00 2.134666091083934e+00 3.69749e-12 7.29750e-11 ----------------------------------------------------------------------------------------------------- 6 Ge 1 -1.257840335701137e+00 -1.257840335701429e+00 2.91545e-13 3.21667e-11 2 2.457899312058505e-01 2.457899311939228e-01 1.19277e-11 2.97465e-12 3 1.553529631484043e+00 1.553529631487152e+00 3.10951e-12 5.77305e-11 ----------------------------------------------------------------------------------------------------- 7 Ge 1 1.049821748720305e-01 1.049821748731180e-01 1.08753e-12 7.01539e-12 2 -2.779692057293122e+00 -2.779692057292131e+00 9.91207e-13 6.70237e-11 3 -3.209360162583986e+00 -3.209360162578487e+00 5.49916e-12 2.13722e-11 ----------------------------------------------------------------------------------------------------- 8 Ge 1 -4.527506167566743e+00 -4.527506167581346e+00 1.46025e-11 2.67667e-09 * 2 -1.959066459046233e+00 -1.959066458915718e+00 1.30515e-10 4.48291e-10 3 6.363098602977231e-01 6.363098602970620e-01 6.61027e-13 9.80722e-11 ----------------------------------------------------------------------------------------------------- 9 Ge 1 -6.868886962418579e-02 -6.868886962070457e-02 3.48122e-12 5.10202e-11 2 -6.134625848188994e+00 -6.134625848186336e+00 2.65832e-12 8.37534e-11 3 1.574676468191140e+00 1.574676468188630e+00 2.50955e-12 7.44207e-11 ----------------------------------------------------------------------------------------------------- 10 Ge 1 -1.615433017691475e-04 -1.615433032475272e-04 1.47838e-12 1.49650e-11 2 1.185360623704747e+00 1.185360623702242e+00 2.50511e-12 1.33624e-11 3 -2.238301406460077e+00 -2.238301406459199e+00 8.77520e-13 6.35270e-12 ----------------------------------------------------------------------------------------------------- 11 Ge 1 -1.378509613056467e+00 -1.378509612176549e+00 8.79918e-10 2.36423e-09 * 2 -8.231510464049871e+00 -8.231510464125998e+00 7.61275e-11 5.28571e-09 * 3 7.221394050209547e-01 7.221394050203365e-01 6.18283e-13 2.25238e-11 ----------------------------------------------------------------------------------------------------- 12 Ge 1 -2.100736892750051e+00 -2.100736892754047e+00 3.99591e-12 1.69177e-10 2 2.292083313048297e+00 2.292083313048842e+00 5.45342e-13 1.96803e-11 3 2.033750501297071e+00 2.033750501317293e+00 2.02220e-11 1.44498e-10 ----------------------------------------------------------------------------------------------------- 13 Ge 1 -1.224354857975823e+00 -1.224354857976960e+00 1.13687e-12 6.79634e-11 2 -9.535089348266931e-01 -9.535089348110493e-01 1.56438e-11 1.90387e-10 3 -4.581518894781873e+00 -4.581518894781116e+00 7.56728e-13 5.93037e-12 ----------------------------------------------------------------------------------------------------- 14 Ge 1 -8.099286395658950e-01 -8.099286395632361e-01 2.65887e-12 1.84770e-10 2 6.996486416731602e-02 6.996486416655703e-02 7.58990e-13 7.10890e-12 3 8.831026984715962e-01 8.831026984715988e-01 2.66454e-15 2.31248e-11 ----------------------------------------------------------------------------------------------------- 15 Ge 1 5.224263511147240e+00 5.224263511141203e+00 6.03695e-12 9.46088e-12 2 5.950399915517089e-01 5.950399915536596e-01 1.95066e-12 1.72043e-10 3 2.885623487990860e+00 2.885623487984626e+00 6.23412e-12 2.39085e-10 ----------------------------------------------------------------------------------------------------- 16 Ge 1 3.594000470993787e+00 3.594000470992410e+00 1.37623e-12 2.42093e-10 2 4.118830670530140e+00 4.118830670549237e+00 1.90976e-11 1.19849e-10 3 4.045334756001064e-01 4.045334756011924e-01 1.08596e-12 9.04428e-11 ----------------------------------------------------------------------------------------------------- 17 Ge 1 3.453652844257438e-01 3.453652844567855e-01 3.10417e-11 8.19178e-10 * 2 3.176018850463834e+00 3.176018850481750e+00 1.79154e-11 1.06844e-10 3 -5.795318512821284e-01 -5.795318512865506e-01 4.42224e-12 5.07477e-11 ----------------------------------------------------------------------------------------------------- 18 Ge 1 1.247808054137688e+00 1.247808054096564e+00 4.11240e-11 6.14813e-11 2 3.348092727451565e+00 3.348092727436715e+00 1.48499e-11 2.47153e-10 3 -1.431478025089243e-01 -1.431478025097935e-01 8.69249e-13 4.69408e-11 ----------------------------------------------------------------------------------------------------- 19 Ge 1 3.860409298492428e+00 3.860409298494075e+00 1.64757e-12 1.98708e-11 2 4.785744855220391e+00 4.785744855213037e+00 7.35412e-12 2.62768e-11 3 -1.311286655224971e+00 -1.311286655230961e+00 5.99010e-12 4.29778e-11 ----------------------------------------------------------------------------------------------------- 20 Ge 1 5.866920949763318e+00 5.866920949754328e+00 8.99014e-12 5.25526e-11 2 1.703399229801146e-01 1.703399229773245e-01 2.79010e-12 9.59299e-11 3 -2.955908590067120e+00 -2.955908590060071e+00 7.04947e-12 1.69298e-10 ----------------------------------------------------------------------------------------------------- 21 Ge 1 -6.214435277050193e+00 -6.214435277049827e+00 3.66818e-13 1.13101e-11 2 3.128358913965226e+00 3.128358913969990e+00 4.76374e-12 2.08384e-11 3 4.460207318264838e+00 4.460207318264785e+00 5.32907e-14 6.28297e-11 ----------------------------------------------------------------------------------------------------- 22 Ge 1 4.636246280042052e-01 4.636246279969970e-01 7.20818e-12 6.11181e-11 2 3.853797801951422e+00 3.853797801949391e+00 2.03082e-12 1.84249e-10 3 5.595882431469740e-01 5.595882431464738e-01 5.00155e-13 1.98533e-11 ----------------------------------------------------------------------------------------------------- 23 Ge 1 -2.670596355458884e+00 -2.670596355467773e+00 8.88845e-12 1.80032e-10 2 2.088273129761054e+00 2.088273129756403e+00 4.65050e-12 1.60987e-11 3 1.054949703024393e+00 1.054949703022920e+00 1.47238e-12 1.37135e-11 ----------------------------------------------------------------------------------------------------- 24 Ge 1 5.931101055688838e-01 5.931101055835022e-01 1.46184e-11 2.88177e-11 2 -1.820128332988441e+00 -1.820128332981879e+00 6.56120e-12 5.20175e-11 3 -6.383697746098449e+00 -6.383697746100494e+00 2.04459e-12 5.79741e-11 ----------------------------------------------------------------------------------------------------- 25 Ge 1 9.466963465756859e-01 9.466963465752429e-01 4.42979e-13 7.90135e-11 2 -4.937183662425470e+00 -4.937183662438080e+00 1.26104e-11 1.70814e-11 3 -1.411426872855779e+00 -1.411426872855279e+00 5.00044e-13 1.52635e-10 ----------------------------------------------------------------------------------------------------- 26 Ge 1 -2.151274548153184e+00 -2.151274548150035e+00 3.14859e-12 2.20743e-11 2 1.906484099132988e+00 1.906484099136018e+00 3.02958e-12 2.79395e-10 3 6.993369335110913e-01 6.993369335174702e-01 6.37890e-12 4.65522e-11 ----------------------------------------------------------------------------------------------------- 27 Ge 1 -4.744270843931657e-01 -4.744270843854512e-01 7.71455e-12 4.48602e-11 2 -6.882657981092802e+00 -6.882657981095581e+00 2.77911e-12 1.88205e-11 3 9.244281352283275e-01 9.244281352318944e-01 3.56692e-12 6.07618e-11 ----------------------------------------------------------------------------------------------------- 28 Ge 1 -1.306290349813898e+00 -1.306290349818602e+00 4.70446e-12 1.56532e-10 2 1.458840586249295e+00 1.458840586252745e+00 3.44968e-12 8.19009e-11 3 -9.486186465308690e-01 -9.486186465410511e-01 1.01821e-11 4.77315e-11 ----------------------------------------------------------------------------------------------------- 29 Ge 1 4.940278568467953e-01 4.940278568088231e-01 3.79722e-11 1.74355e-11 2 -3.149581158794322e+00 -3.149581158803236e+00 8.91376e-12 5.56000e-11 3 2.236155841979921e-01 2.236155841964855e-01 1.50666e-12 1.35910e-10 ----------------------------------------------------------------------------------------------------- 30 Ge 1 -5.897176957723593e-01 -5.897176957689454e-01 3.41394e-12 1.50928e-11 2 -1.251676144083923e+00 -1.251676144084075e+00 1.52101e-13 5.93181e-11 3 -2.061765977911636e+00 -2.061765977890842e+00 2.07940e-11 8.38365e-11 ----------------------------------------------------------------------------------------------------- 31 Ge 1 -3.372473565223340e+00 -3.372473565224286e+00 9.46798e-13 3.84910e-11 2 -3.701671718596906e+00 -3.701671718606070e+00 9.16422e-12 9.15441e-11 3 1.151737165398837e+00 1.151737165401997e+00 3.15969e-12 1.54220e-10 ----------------------------------------------------------------------------------------------------- 32 Ge 1 4.029961500152606e-01 4.029961500144267e-01 8.33833e-13 4.30805e-12 2 -1.179060475893573e-01 -1.179060475893250e-01 3.23630e-14 2.32276e-11 3 8.053657193905650e-01 8.053657193913958e-01 8.30780e-13 2.25330e-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 discontinuities. Maximum error obtained for particle = 10, direction = 1: |F_model - F_numer| error = ----------------------- = 9.15160e-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 = Si | a0 = 3.8974828720092773 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 2.711285960934922e+00 2.711285960921505e+00 1.34168e-11 4.55360e-11 2 1.009625721351997e+00 1.009625721354256e+00 2.25819e-12 1.83813e-11 3 3.076829291992808e+00 3.076829291996434e+00 3.62554e-12 5.37570e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -1.388159386243227e+00 -1.388159386239543e+00 3.68461e-12 7.76770e-11 2 -2.907177501964957e+00 -2.907177502018566e+00 5.36087e-11 2.12819e-07 * 3 -1.345786119002531e+00 -1.345786119006511e+00 3.98015e-12 7.53306e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 -3.660428119021045e+00 -3.660428119027585e+00 6.54055e-12 1.03253e-10 2 -7.169435425466459e-01 -7.169435425416022e-01 5.04374e-12 1.38549e-11 3 -1.817180261366520e+00 -1.817180261350221e+00 1.62985e-11 1.62340e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 5.737147866426652e-01 5.737147866259725e-01 1.66926e-11 3.15415e-11 2 1.824188813771095e-01 1.824188813780364e-01 9.26870e-13 8.31525e-11 3 -4.228543040710244e-01 -4.228543040664424e-01 4.58195e-12 3.53723e-12 ----------------------------------------------------------------------------------------------------- 5 Si 1 1.534993485334417e+00 1.534993485324064e+00 1.03535e-11 3.06724e-11 2 1.366013081590292e+00 1.366013081575587e+00 1.47049e-11 4.49869e-11 3 2.030468573265205e+00 2.030468573266685e+00 1.48015e-12 7.31028e-10 * ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.935465393636411e+00 -2.935465393631230e+00 5.18119e-12 4.16955e-11 2 1.839798152515221e+00 1.839798152516062e+00 8.41771e-13 1.94949e-11 3 1.906987173210963e+00 1.906987173194085e+00 1.68781e-11 6.56126e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -4.088611280348363e+00 -4.088611280348132e+00 2.31815e-13 1.97717e-11 2 1.239837868240525e+00 1.239837868240997e+00 4.71845e-13 8.25862e-11 3 -2.824630494729440e+00 -2.824630494729861e+00 4.20552e-13 9.97824e-12 ----------------------------------------------------------------------------------------------------- 8 Si 1 2.621013602489139e+00 2.621013602506625e+00 1.74860e-11 1.47760e-10 2 -8.853245509212393e-01 -8.853245509218365e-01 5.97189e-13 3.70899e-10 * 3 2.913038985946633e+00 2.913038985943885e+00 2.74802e-12 2.01981e-11 ----------------------------------------------------------------------------------------------------- 9 Si 1 4.639670973730757e-01 4.639670973758224e-01 2.74669e-12 8.16970e-11 2 8.622473439373881e-01 8.622473439374005e-01 1.24345e-14 8.59561e-11 3 6.775212211145458e-01 6.775212211195483e-01 5.00244e-12 1.06894e-10 ----------------------------------------------------------------------------------------------------- 10 Si 1 1.051248188522415e+00 1.051248188523504e+00 1.08935e-12 3.43576e-11 2 3.239656676092565e+00 3.239656676089792e+00 2.77289e-12 2.21196e-11 3 -4.405546365105501e+00 -4.405546365106976e+00 1.47526e-12 5.69766e-12 ----------------------------------------------------------------------------------------------------- 11 Si 1 -3.136163620467222e+00 -3.136163620448979e+00 1.82427e-11 3.13426e-10 2 -6.169799023385339e+00 -6.169799023402263e+00 1.69234e-11 8.54987e-11 3 4.641915631944069e+00 4.641915631955195e+00 1.11262e-11 2.92554e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 -1.785044886898470e+00 -1.785044886899840e+00 1.36979e-12 2.52318e-11 2 -3.710481826165024e-01 -3.710481826030693e-01 1.34331e-11 1.16656e-10 3 -6.208165244517588e-01 -6.208165244562149e-01 4.45610e-12 6.03347e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 7.160177802149655e+00 7.160177802157961e+00 8.30536e-12 4.25615e-11 2 1.128067802767998e+00 1.128067802770359e+00 2.36033e-12 4.06384e-11 3 8.888653177063017e-01 8.888653177039544e-01 2.34734e-12 1.16973e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 -6.472514502236953e-01 -6.472514502248782e-01 1.18283e-12 7.46148e-12 2 -2.348683611547764e-02 -2.348683611540770e-02 6.99406e-14 4.82402e-12 3 5.837925785676595e-01 5.837925785687412e-01 1.08169e-12 1.69601e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 -1.339022157998923e+00 -1.339022158007679e+00 8.75566e-12 1.03033e-10 2 4.557132097680384e+00 4.557132097681008e+00 6.24389e-13 6.44045e-11 3 8.277820061607608e-01 8.277820061507126e-01 1.00482e-11 6.08055e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 3.295790465321367e+00 3.295790465311499e+00 9.86811e-12 3.24443e-11 2 -1.152328831590232e+00 -1.152328831581144e+00 9.08762e-12 4.75304e-11 3 2.994639453047198e+00 2.994639453053887e+00 6.68887e-12 3.74909e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 6.757217684182137e-01 6.757217684210880e-01 2.87426e-12 1.37781e-11 2 1.189624808769604e-01 1.189624808776736e-01 7.13138e-13 8.72223e-12 3 -5.892342102924923e-01 -5.892342102919363e-01 5.56000e-13 8.98803e-12 ----------------------------------------------------------------------------------------------------- 18 Si 1 -1.493081066237730e+00 -1.493081066251322e+00 1.35916e-11 4.38194e-11 2 -1.846863351326197e-01 -1.846863351285561e-01 4.06358e-12 1.30478e-10 3 3.122478229376963e+00 3.122478229380859e+00 3.89599e-12 6.86047e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 1.180556399249872e+00 1.180556399254997e+00 5.12523e-12 4.52249e-11 2 7.360107545968379e+00 7.360107545969957e+00 1.57829e-12 1.00361e-10 3 -4.064947543545832e+00 -4.064947543545160e+00 6.71463e-13 3.28475e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 2.817169470710407e+00 2.817169470713678e+00 3.27027e-12 3.44227e-11 2 -1.992814101379869e+00 -1.992814101378232e+00 1.63780e-12 2.30989e-11 3 2.161440523191434e-01 2.161440523265790e-01 7.43561e-12 1.16164e-10 ----------------------------------------------------------------------------------------------------- 21 Si 1 -5.386365548868540e+00 -5.386365548872013e+00 3.47367e-12 1.23506e-10 2 5.004067551945986e-02 5.004067550629356e-02 1.31663e-11 7.68954e-11 3 -1.314787518339779e+00 -1.314787518351246e+00 1.14666e-11 6.92533e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 2.710065699799043e-01 2.710065699790867e-01 8.17624e-13 1.56488e-10 2 1.791818062161683e+00 1.791818062164076e+00 2.39364e-12 2.81770e-11 3 -3.300135424407539e+00 -3.300135424395273e+00 1.22662e-11 1.99477e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 2.233295893135177e+00 2.233295893132705e+00 2.47224e-12 9.54121e-11 2 -5.968286462017766e-01 -5.968286461988028e-01 2.97373e-12 1.91039e-11 3 4.676422519126538e+00 4.676422519128431e+00 1.89360e-12 6.16032e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -1.342271719654059e+00 -1.342271719651443e+00 2.61657e-12 1.10307e-11 2 2.928182242852157e+00 2.928182242852081e+00 7.63833e-14 9.07341e-11 3 -1.461022401781177e+00 -1.461022401793902e+00 1.27254e-11 1.07505e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.925624580165909e+00 -1.925624580165406e+00 5.03153e-13 8.72877e-10 * 2 -3.883414680501481e+00 -3.883414680525266e+00 2.37854e-11 3.54118e-10 * 3 -5.583503401789383e+00 -5.583503401792681e+00 3.29781e-12 1.49300e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 2.218985571530465e+00 2.218985571529492e+00 9.73444e-13 8.85350e-11 2 2.252234978414685e+00 2.252234978388743e+00 2.59424e-11 1.34590e-11 3 1.510018089136489e+00 1.510018089134411e+00 2.07767e-12 1.50044e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 1.055330958851269e+01 1.055330958850737e+01 5.32197e-12 1.38582e-10 2 -4.797627971663085e+00 -4.797627971654167e+00 8.91820e-12 4.19284e-10 * 3 3.301669734269864e+00 3.301669734266230e+00 3.63398e-12 2.17741e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 5.892987610266430e-01 5.892987610260610e-01 5.81979e-13 4.29361e-11 2 -1.136527984873892e-01 -1.136527984845802e-01 2.80902e-12 3.88764e-11 3 -2.211803462035550e+00 -2.211803462041981e+00 6.43130e-12 1.33473e-10 ----------------------------------------------------------------------------------------------------- 29 Si 1 -3.821041099756698e+00 -3.821041099755369e+00 1.32871e-12 2.12808e-10 2 1.306155412388078e-02 1.306155413319635e-02 9.31558e-12 2.73161e-10 3 1.098256046051732e+00 1.098256046039929e+00 1.18030e-11 1.00889e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 -4.269495192204047e+00 -4.269495192206046e+00 1.99840e-12 8.69447e-11 2 -4.354049077667213e+00 -4.354049077666553e+00 6.59917e-13 7.31708e-11 3 -5.296044485595479e+00 -5.296044485601549e+00 6.07070e-12 2.68736e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -5.963771520031301e+00 -5.963771520024388e+00 6.91269e-12 8.03491e-11 2 5.788635906680850e-01 5.788635906613554e-01 6.72962e-12 7.37796e-11 3 6.807519159373641e-01 6.807519159209090e-01 1.64551e-11 3.65566e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.230261610424622e+00 3.230261610409876e+00 1.47469e-11 7.94453e-11 2 -2.368886675964938e+00 -2.368886675974342e+00 9.40403e-12 8.12932e-11 3 1.107116973397652e-01 1.107116973305090e-01 9.25621e-12 3.00897e-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 = 29, direction = 2: |F_model - F_numer| error = ----------------------- = 7.13206e-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. MIXED STRUCTURE -- Species = Ge Si | a0 = 3.9462408611748288 | (Configuration in file "config-GeSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -9.619583683700919e-01 -9.619583683593015e-01 1.07904e-11 1.10573e-10 2 -4.419885242518684e-01 -4.419885242494211e-01 2.44726e-12 6.41420e-12 3 -7.684395851995764e-01 -7.684395851979742e-01 1.60227e-12 1.73545e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -3.752990748118234e+00 -3.752990748131165e+00 1.29305e-11 2.69079e-10 2 4.084935012142576e+00 4.084935012136187e+00 6.38867e-12 2.07718e-11 3 -9.585554497950586e-01 -9.585554497913991e-01 3.65952e-12 3.87446e-12 ----------------------------------------------------------------------------------------------------- 3 Ge 1 1.064730834261852e+00 1.064730834257246e+00 4.60609e-12 9.86617e-11 2 -2.583897671615959e+00 -2.583897671616774e+00 8.14460e-13 4.53237e-12 3 1.248346171118795e+00 1.248346171114545e+00 4.25038e-12 2.98224e-11 ----------------------------------------------------------------------------------------------------- 4 Ge 1 8.453458264934581e-02 8.453458264050570e-02 8.84011e-12 1.54171e-11 2 1.325505130818224e+00 1.325505130855164e+00 3.69400e-11 2.09015e-10 3 5.098853263918870e-01 5.098853263890286e-01 2.85838e-12 6.52124e-11 ----------------------------------------------------------------------------------------------------- 5 Ge 1 6.174305603570173e+00 6.174305603572593e+00 2.42029e-12 8.46025e-11 2 2.061601357881707e+00 2.061601357877561e+00 4.14602e-12 2.47189e-11 3 4.033080447686298e+00 4.033080447675262e+00 1.10356e-11 8.12230e-11 ----------------------------------------------------------------------------------------------------- 6 Ge 1 -1.307320132614258e+00 -1.307320132615480e+00 1.22280e-12 2.94678e-11 2 -1.723149601481510e+00 -1.723149601484868e+00 3.35798e-12 6.59997e-11 3 3.810382486121838e-01 3.810382486027371e-01 9.44667e-12 1.70680e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -5.627032438346701e+00 -5.627032438347840e+00 1.13864e-12 2.76477e-10 2 3.995984980976269e+00 3.995984980980181e+00 3.91154e-12 2.14362e-11 3 -2.267921086344931e+00 -2.267921086345803e+00 8.72635e-13 2.30305e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 2.320741246654468e+00 2.320741246757116e+00 1.02648e-10 9.21667e-11 2 -1.617212922927009e+00 -1.617212923098034e+00 1.71025e-10 3.39358e-10 3 3.275067947495161e+00 3.275067947494483e+00 6.77680e-13 1.47000e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 2.466859390109191e+00 2.466859390108885e+00 3.06422e-13 6.38720e-11 2 -1.233992430757515e+00 -1.233992430750029e+00 7.48623e-12 4.89173e-11 3 -7.454923740805344e-02 -7.454923739862519e-02 9.42825e-12 1.54302e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 5.341120679235761e+00 5.341120679240030e+00 4.26859e-12 1.63303e-09 * 2 -4.358030611033792e+00 -4.358030611037247e+00 3.45501e-12 6.83453e-12 3 3.523003320293057e+00 3.523003320295580e+00 2.52331e-12 7.86282e-11 ----------------------------------------------------------------------------------------------------- 11 Ge 1 1.309908520080328e+00 1.309908520097768e+00 1.74398e-11 3.59519e-10 * 2 -2.087609839980404e+00 -2.087609840010786e+00 3.03819e-11 5.75206e-10 * 3 -2.111948801337255e+00 -2.111948801340669e+00 3.41371e-12 1.01617e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 2.057589011685078e-01 2.057589011677638e-01 7.43988e-13 1.29391e-11 2 -4.475728600224085e-01 -4.475728600233382e-01 9.29701e-13 4.55430e-11 3 -1.297165305633821e+00 -1.297165305630574e+00 3.24740e-12 6.57838e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -4.936313841584451e+00 -4.936313841594153e+00 9.70157e-12 1.12790e-10 2 7.126596855371838e+00 7.126596855376511e+00 4.67359e-12 1.70566e-11 3 2.169244547434653e+00 2.169244547426616e+00 8.03713e-12 1.96357e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 2 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 3 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 ----------------------------------------------------------------------------------------------------- 15 Ge 1 -9.663275615985436e-01 -9.663275616131103e-01 1.45667e-11 5.46790e-11 2 1.618050694298244e+00 1.618050694296619e+00 1.62426e-12 2.12947e-11 3 6.465488898426823e-01 6.465488898488109e-01 6.12854e-12 4.32449e-11 ----------------------------------------------------------------------------------------------------- 16 Ge 1 -2.164014558814236e+00 -2.164014558821210e+00 6.97442e-12 1.75318e-11 2 -5.199576253410824e-01 -5.199576253438642e-01 2.78189e-12 5.15147e-11 3 -5.744844819571722e+00 -5.744844819569221e+00 2.50111e-12 4.54978e-11 ----------------------------------------------------------------------------------------------------- 17 Ge 1 1.237745362584834e+00 1.237745362580855e+00 3.97904e-12 1.52982e-11 2 1.273344471250780e+00 1.273344471251435e+00 6.54810e-13 5.51690e-11 3 9.872684151082424e-04 9.872684166133967e-04 1.50515e-12 1.46561e-11 ----------------------------------------------------------------------------------------------------- 18 Ge 1 -2.251386439627901e+00 -2.251386439617485e+00 1.04166e-11 4.59188e-11 2 -6.302158000506632e+00 -6.302158000510781e+00 4.14868e-12 1.14428e-10 3 -2.911093749673771e+00 -2.911093749688043e+00 1.42726e-11 3.85820e-10 * ----------------------------------------------------------------------------------------------------- 19 Si 1 6.724627228308613e-01 6.724627228145612e-01 1.63001e-11 1.46112e-11 2 1.599364762666406e+00 1.599364762679548e+00 1.31417e-11 1.24043e-11 3 -2.397497672724020e+00 -2.397497672730636e+00 6.61560e-12 8.48752e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 3.790449787606778e+00 3.790449787602025e+00 4.75309e-12 6.16125e-11 2 4.532522146621262e+00 4.532522146609152e+00 1.21103e-11 6.12266e-11 3 -2.533577238784870e+00 -2.533577238782202e+00 2.66764e-12 3.76152e-11 ----------------------------------------------------------------------------------------------------- 21 Ge 1 -7.699316830387516e-01 -7.699316830409365e-01 2.18492e-12 1.17960e-10 2 -2.669999338045209e-01 -2.669999338086407e-01 4.11982e-12 3.32371e-11 3 -5.024060986163881e-01 -5.024060986167459e-01 3.57825e-13 2.61063e-11 ----------------------------------------------------------------------------------------------------- 22 Ge 1 -4.625114380114831e-01 -4.625114380060453e-01 5.43787e-12 6.42908e-11 2 -3.296650832501850e+00 -3.296650832534165e+00 3.23150e-11 1.30846e-10 3 1.384474729283812e+00 1.384474729279655e+00 4.15734e-12 6.86475e-11 ----------------------------------------------------------------------------------------------------- 23 Ge 1 1.050604163591629e+00 1.050604163591976e+00 3.46612e-13 1.93296e-11 2 1.247506586460626e+00 1.247506586482856e+00 2.22293e-11 9.39915e-11 3 -6.760980170192226e-01 -6.760980170238973e-01 4.67471e-12 1.37916e-10 ----------------------------------------------------------------------------------------------------- 24 Ge 1 3.348394751670194e+00 3.348394751718819e+00 4.86251e-11 9.58806e-11 2 3.731736934480860e+00 3.731736934753560e+00 2.72700e-10 6.76484e-10 * 3 5.418270111446246e-01 5.418270111439997e-01 6.24945e-13 8.62033e-11 ----------------------------------------------------------------------------------------------------- 25 Ge 1 -3.761373846233127e+00 -3.761373846227574e+00 5.55289e-12 4.44054e-11 2 -1.140788258055740e+00 -1.140788258049171e+00 6.56897e-12 1.26428e-10 3 1.876945022817374e+00 1.876945022804841e+00 1.25333e-11 1.07108e-10 ----------------------------------------------------------------------------------------------------- 26 Ge 1 6.817270217723317e-01 6.817270217716559e-01 6.75793e-13 4.70856e-11 2 2.633557875670104e+00 2.633557875668343e+00 1.76081e-12 1.50009e-11 3 2.675748703919659e-02 2.675748703876203e-02 4.34559e-13 1.10255e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 -1.755468165466379e+00 -1.755468165197313e+00 2.69066e-10 5.87013e-10 * 2 2.030127605035938e+00 2.030127605021483e+00 1.44547e-11 6.04911e-10 * 3 6.716518309642331e+00 6.716518309657859e+00 1.55280e-11 8.11546e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 9.778784535891398e-01 9.778784535850027e-01 4.13714e-12 2.92864e-11 2 -2.715121046629529e+00 -2.715121046639872e+00 1.03437e-11 7.52163e-11 3 -1.504061663586100e+00 -1.504061663585782e+00 3.18856e-13 9.44089e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 6.199115770322010e-01 6.199115770160618e-01 1.61392e-11 3.15453e-11 2 -1.843086275804246e+00 -1.843086275807340e+00 3.09464e-12 8.44900e-11 3 6.045487947340582e-01 6.045487947595684e-01 2.55101e-11 1.28273e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 1.450744634198010e+00 1.450744634193735e+00 4.27480e-12 9.04363e-11 2 -2.054728198572494e+00 -2.054728198577672e+00 5.17808e-12 9.84004e-11 3 -2.627277880684672e+00 -2.627277880675075e+00 9.59721e-12 7.59282e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -2.760688544864274e+00 -2.760688544882059e+00 1.77849e-11 1.44412e-10 2 -2.800369818105775e+00 -2.800369818103288e+00 2.48690e-12 3.98961e-11 3 -5.030596116340874e-01 -5.030596116333328e-01 7.54619e-13 8.91170e-11 ----------------------------------------------------------------------------------------------------- 32 Ge 1 -1.320560465917175e+00 -1.320560465919088e+00 1.91269e-12 2.46146e-10 2 -1.827519962282491e+00 -1.827519962306466e+00 2.39748e-11 5.69700e-11 3 -5.977730393767927e-02 -5.977730393493624e-02 2.74303e-12 4.34473e-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 discontinuities. Maximum error obtained for particle = 17, direction = 3: |F_model - F_numer| error = ----------------------- = 1.52456e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 9.15160e-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: B Comment: The letter grade B was assigned because the normalized error in the computation was 9.15160e-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.