!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_002 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 6.060735949464214e+00 8.43769e-13 5.46336e-11 2 3.041304174181283e+00 3.041304174180518e+00 7.64722e-13 1.71250e-11 3 1.987445885979092e+00 1.987445885971860e+00 7.23133e-12 8.90272e-11 ----------------------------------------------------------------------------------------------------- 2 Ge 1 -4.059738781400134e+00 -4.059738781400328e+00 1.93623e-13 1.38511e-10 2 5.018433045807429e-01 5.018433045827727e-01 2.02982e-12 3.29661e-11 3 3.037905524703527e+00 3.037905524693137e+00 1.03904e-11 5.69114e-11 ----------------------------------------------------------------------------------------------------- 3 Ge 1 -1.078366292286802e+00 -1.078366292287516e+00 7.14095e-13 1.05069e-09 * 2 5.231383323832909e-01 5.231383323762547e-01 7.03615e-12 1.24649e-10 3 -3.884089201701975e+00 -3.884089201687206e+00 1.47695e-11 7.33347e-11 ----------------------------------------------------------------------------------------------------- 4 Ge 1 4.467527525378215e+00 4.467527525380316e+00 2.10054e-12 8.53104e-11 2 4.814230425684749e+00 4.814230425683317e+00 1.43174e-12 1.30803e-10 3 1.975741975728411e+00 1.975741975728974e+00 5.62883e-13 1.58904e-11 ----------------------------------------------------------------------------------------------------- 5 Ge 1 -3.874214365923032e-01 -3.874214365937938e-01 1.49059e-12 2.04153e-10 2 6.156722907621346e-01 6.156722907574418e-01 4.69280e-12 2.70585e-11 3 2.134666091080236e+00 2.134666091083932e+00 3.69571e-12 7.29745e-11 ----------------------------------------------------------------------------------------------------- 6 Ge 1 -1.257840335701137e+00 -1.257840335701428e+00 2.90434e-13 3.21663e-11 2 2.457899312058505e-01 2.457899312077609e-01 1.91039e-12 4.17063e-11 3 1.553529631484043e+00 1.553529631476376e+00 7.66609e-12 1.93647e-11 ----------------------------------------------------------------------------------------------------- 7 Ge 1 1.049821748720305e-01 1.049821748731179e-01 1.08748e-12 7.01546e-12 2 -2.779692057293122e+00 -2.779692057292129e+00 9.92983e-13 6.70197e-11 3 -3.209360162583986e+00 -3.209360162578489e+00 5.49738e-12 2.13722e-11 ----------------------------------------------------------------------------------------------------- 8 Ge 1 -4.527506167566743e+00 -4.527506167580341e+00 1.35971e-11 2.67393e-09 * 2 -1.959066459046233e+00 -1.959066459129783e+00 8.35503e-11 4.69245e-10 * 3 6.363098602977231e-01 6.363098603002104e-01 2.48734e-12 6.19512e-11 ----------------------------------------------------------------------------------------------------- 9 Ge 1 -6.868886962418579e-02 -6.868886962070461e-02 3.48117e-12 5.10202e-11 2 -6.134625848188994e+00 -6.134625848186332e+00 2.66187e-12 8.37579e-11 3 1.574676468191140e+00 1.574676468188629e+00 2.51066e-12 7.44207e-11 ----------------------------------------------------------------------------------------------------- 10 Ge 1 -1.615433017704729e-04 -1.615433032475271e-04 1.47705e-12 1.49650e-11 2 1.185360623704747e+00 1.185360623702242e+00 2.50577e-12 1.33618e-11 3 -2.238301406460079e+00 -2.238301406459198e+00 8.81073e-13 6.35358e-12 ----------------------------------------------------------------------------------------------------- 11 Ge 1 -1.378509613056467e+00 -1.378509612176548e+00 8.79919e-10 2.36423e-09 * 2 -8.231510464049871e+00 -8.231510464105028e+00 5.51577e-11 4.74376e-09 * 3 7.221394050209547e-01 7.221394050203368e-01 6.17950e-13 2.25235e-11 ----------------------------------------------------------------------------------------------------- 12 Ge 1 -2.100736892750051e+00 -2.100736892754046e+00 3.99458e-12 1.69176e-10 2 2.292083313048297e+00 2.292083313048840e+00 5.43565e-13 1.96798e-11 3 2.033750501297071e+00 2.033750501315494e+00 1.84230e-11 1.06461e-10 ----------------------------------------------------------------------------------------------------- 13 Ge 1 -1.224354857975823e+00 -1.224354857983708e+00 7.88480e-12 1.08283e-10 2 -9.535089348266931e-01 -9.535089348110497e-01 1.56434e-11 1.90386e-10 3 -4.581518894781869e+00 -4.581518894781114e+00 7.54952e-13 5.93481e-12 ----------------------------------------------------------------------------------------------------- 14 Ge 1 -8.099286395658950e-01 -8.099286395583696e-01 7.52542e-12 2.30510e-10 2 6.996486416731602e-02 6.996486416655699e-02 7.59032e-13 7.10890e-12 3 8.831026984715962e-01 8.831026984743705e-01 2.77434e-12 2.92119e-11 ----------------------------------------------------------------------------------------------------- 15 Ge 1 5.224263511147240e+00 5.224263511141199e+00 6.04050e-12 9.45999e-12 2 5.950399915517089e-01 5.950399915537429e-01 2.03393e-12 1.72560e-10 3 2.885623487990860e+00 2.885623487995592e+00 4.73177e-12 1.73536e-10 ----------------------------------------------------------------------------------------------------- 16 Ge 1 3.594000470993787e+00 3.594000470992407e+00 1.37934e-12 2.42094e-10 2 4.118830670530140e+00 4.118830670549239e+00 1.90994e-11 1.19849e-10 3 4.045334756001082e-01 4.045334756011927e-01 1.08452e-12 9.04426e-11 ----------------------------------------------------------------------------------------------------- 17 Ge 1 3.453652844257438e-01 3.453652844567853e-01 3.10415e-11 8.19178e-10 * 2 3.176018850463834e+00 3.176018850481748e+00 1.79132e-11 1.06847e-10 3 -5.795318512821284e-01 -5.795318512865503e-01 4.42191e-12 5.07479e-11 ----------------------------------------------------------------------------------------------------- 18 Ge 1 1.247808054137688e+00 1.247808054096563e+00 4.11251e-11 6.14806e-11 2 3.348092727451565e+00 3.348092727436712e+00 1.48530e-11 2.47152e-10 3 -1.431478025089243e-01 -1.431478025097936e-01 8.69332e-13 4.69408e-11 ----------------------------------------------------------------------------------------------------- 19 Ge 1 3.860409298492428e+00 3.860409298494078e+00 1.64979e-12 1.98699e-11 2 4.785744855220391e+00 4.785744855213039e+00 7.35145e-12 2.62776e-11 3 -1.311286655224971e+00 -1.311286655230962e+00 5.99054e-12 4.29783e-11 ----------------------------------------------------------------------------------------------------- 20 Ge 1 5.866920949763318e+00 5.866920949754331e+00 8.98748e-12 5.25553e-11 2 1.703399229801146e-01 1.703399229773246e-01 2.79005e-12 9.59300e-11 3 -2.955908590067120e+00 -2.955908590060072e+00 7.04814e-12 1.69299e-10 ----------------------------------------------------------------------------------------------------- 21 Ge 1 -6.214435277050193e+00 -6.214435277049821e+00 3.72147e-13 1.13021e-11 2 3.128358913965226e+00 3.128358913969991e+00 4.76508e-12 2.08371e-11 3 4.460207318264838e+00 4.460207318264782e+00 5.59552e-14 6.28280e-11 ----------------------------------------------------------------------------------------------------- 22 Ge 1 4.636246280042052e-01 4.636246280001564e-01 4.04882e-12 9.38054e-11 2 3.853797801951422e+00 3.853797801953822e+00 2.39986e-12 8.77556e-11 3 5.595882431469740e-01 5.595882431464735e-01 5.00489e-13 1.98536e-11 ----------------------------------------------------------------------------------------------------- 23 Ge 1 -2.670596355458884e+00 -2.670596355467774e+00 8.88978e-12 1.80032e-10 2 2.088273129761054e+00 2.088273129756402e+00 4.65183e-12 1.60987e-11 3 1.054949703024393e+00 1.054949703022921e+00 1.47193e-12 1.37137e-11 ----------------------------------------------------------------------------------------------------- 24 Ge 1 5.931101055688838e-01 5.931101055835015e-01 1.46178e-11 2.88175e-11 2 -1.820128332988441e+00 -1.820128332981880e+00 6.56053e-12 5.20168e-11 3 -6.383697746098449e+00 -6.383697746100490e+00 2.04015e-12 5.79723e-11 ----------------------------------------------------------------------------------------------------- 25 Ge 1 9.466963465756859e-01 9.466963465752434e-01 4.42535e-13 7.90135e-11 2 -4.937183662425470e+00 -4.937183662438083e+00 1.26130e-11 1.70788e-11 3 -1.411426872855779e+00 -1.411426872855280e+00 4.99156e-13 1.52635e-10 ----------------------------------------------------------------------------------------------------- 26 Ge 1 -2.151274548153184e+00 -2.151274548158320e+00 5.13589e-12 3.30124e-09 * 2 1.906484099132988e+00 1.906484099136016e+00 3.02802e-12 2.79395e-10 3 6.993369335110913e-01 6.993369335174704e-01 6.37912e-12 4.65517e-11 ----------------------------------------------------------------------------------------------------- 27 Ge 1 -4.744270843931657e-01 -4.744270843854508e-01 7.71494e-12 4.48599e-11 2 -6.882657981092802e+00 -6.882657981095578e+00 2.77645e-12 1.88187e-11 3 9.244281352283275e-01 9.244281352318948e-01 3.56737e-12 6.07618e-11 ----------------------------------------------------------------------------------------------------- 28 Ge 1 -1.306290349813898e+00 -1.306290349818602e+00 4.70357e-12 1.56535e-10 2 1.458840586249295e+00 1.458840586252746e+00 3.45057e-12 8.19009e-11 3 -9.486186465308690e-01 -9.486186465410515e-01 1.01825e-11 4.77317e-11 ----------------------------------------------------------------------------------------------------- 29 Ge 1 4.940278568467953e-01 4.940278568272949e-01 1.95004e-11 3.32040e-11 2 -3.149581158794322e+00 -3.149581158800439e+00 6.11733e-12 1.29283e-11 3 2.236155841979921e-01 2.236155841964856e-01 1.50654e-12 1.35910e-10 ----------------------------------------------------------------------------------------------------- 30 Ge 1 -5.897176957723593e-01 -5.897176957689449e-01 3.41438e-12 1.50920e-11 2 -1.251676144083923e+00 -1.251676144084074e+00 1.50990e-13 5.93179e-11 3 -2.061765977911636e+00 -2.061765977914669e+00 3.03269e-12 2.21543e-11 ----------------------------------------------------------------------------------------------------- 31 Ge 1 -3.372473565223340e+00 -3.372473565224288e+00 9.48575e-13 3.84901e-11 2 -3.701671718596906e+00 -3.701671718606072e+00 9.16600e-12 9.15441e-11 3 1.151737165398837e+00 1.151737165401998e+00 3.16036e-12 1.54220e-10 ----------------------------------------------------------------------------------------------------- 32 Ge 1 4.029961500152606e-01 4.029961500144265e-01 8.34055e-13 4.30822e-12 2 -1.179060475893573e-01 -1.179060475893249e-01 3.24463e-14 2.32276e-11 3 8.053657193905650e-01 8.053657193913962e-01 8.31224e-13 2.25332e-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 = ----------------------- = 9.14340e-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 2.711285960921503e+00 1.34182e-11 4.55374e-11 2 1.009625721351997e+00 1.009625721354255e+00 2.25753e-12 1.83813e-11 3 3.076829291992808e+00 3.076829291996432e+00 3.62421e-12 5.37566e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -1.388159386243227e+00 -1.388159386239544e+00 3.68372e-12 7.76768e-11 2 -2.907177501964957e+00 -2.907177502018567e+00 5.36100e-11 2.12819e-07 * 3 -1.345786119002531e+00 -1.345786119006509e+00 3.97882e-12 7.53306e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 -3.660428119021045e+00 -3.660428119027582e+00 6.53744e-12 1.03249e-10 2 -7.169435425466459e-01 -7.169435425416018e-01 5.04419e-12 1.38544e-11 3 -1.817180261366520e+00 -1.817180261350222e+00 1.62976e-11 1.62340e-10 ----------------------------------------------------------------------------------------------------- 4 Si 1 5.737147866426652e-01 5.737147866259726e-01 1.66925e-11 3.15414e-11 2 1.824188813771095e-01 1.824188813780363e-01 9.26786e-13 8.31526e-11 3 -4.228543040710244e-01 -4.228543040664421e-01 4.58222e-12 3.53723e-12 ----------------------------------------------------------------------------------------------------- 5 Si 1 1.534993485334417e+00 1.534993485324063e+00 1.03544e-11 3.06724e-11 2 1.366013081590292e+00 1.366013081575586e+00 1.47058e-11 4.49869e-11 3 2.030468573265205e+00 2.030468573266684e+00 1.47882e-12 7.31028e-10 * ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.935465393636411e+00 -2.935465393631228e+00 5.18297e-12 4.16951e-11 2 1.839798152515221e+00 1.839798152516061e+00 8.40661e-13 1.94951e-11 3 1.906987173210963e+00 1.906987173194083e+00 1.68794e-11 6.56126e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -4.088611280348363e+00 -4.088611280348129e+00 2.34479e-13 1.97717e-11 2 1.239837868240525e+00 1.239837868240998e+00 4.72289e-13 8.25868e-11 3 -2.824630494729440e+00 -2.824630494729859e+00 4.18332e-13 9.98090e-12 ----------------------------------------------------------------------------------------------------- 8 Si 1 2.621013602489139e+00 2.621013602506622e+00 1.74838e-11 1.47762e-10 2 -8.853245509212393e-01 -8.853245509218358e-01 5.96523e-13 3.70899e-10 * 3 2.913038985946633e+00 2.913038985943882e+00 2.75069e-12 2.01945e-11 ----------------------------------------------------------------------------------------------------- 9 Si 1 4.639670973730757e-01 4.639670973758221e-01 2.74636e-12 8.16967e-11 2 8.622473439373881e-01 8.622473439374009e-01 1.27676e-14 8.59567e-11 3 6.775212211145458e-01 6.775212211195486e-01 5.00278e-12 1.06894e-10 ----------------------------------------------------------------------------------------------------- 10 Si 1 1.051248188522415e+00 1.051248188523503e+00 1.08868e-12 3.43598e-11 2 3.239656676092565e+00 3.239656676089794e+00 2.77156e-12 2.21205e-11 3 -4.405546365105501e+00 -4.405546365106973e+00 1.47260e-12 5.69589e-12 ----------------------------------------------------------------------------------------------------- 11 Si 1 -3.136163620467222e+00 -3.136163620448976e+00 1.82454e-11 3.13426e-10 2 -6.169799023385339e+00 -6.169799023402259e+00 1.69198e-11 8.55005e-11 3 4.641915631944069e+00 4.641915631955062e+00 1.09930e-11 2.92665e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 -1.785044886898470e+00 -1.785044886899841e+00 1.37068e-12 2.52318e-11 2 -3.710481826165024e-01 -3.710481826030695e-01 1.34329e-11 1.16656e-10 3 -6.208165244517588e-01 -6.208165244562153e-01 4.45644e-12 6.03350e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 7.160177802149655e+00 7.160177802157964e+00 8.30891e-12 4.25615e-11 2 1.128067802767998e+00 1.128067802770358e+00 2.35922e-12 4.06375e-11 3 8.888653177063017e-01 8.888653177039538e-01 2.34790e-12 1.16973e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 -6.472514502236953e-01 -6.472514502248777e-01 1.18239e-12 7.46037e-12 2 -2.348683611547764e-02 -2.348683611540772e-02 6.99267e-14 4.82402e-12 3 5.837925785676595e-01 5.837925785687416e-01 1.08202e-12 1.69599e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 -1.339022157998923e+00 -1.339022158007680e+00 8.75633e-12 1.03033e-10 2 4.557132097680384e+00 4.557132097681005e+00 6.20837e-13 6.44018e-11 3 8.277820061607608e-01 8.277820061507130e-01 1.00479e-11 6.08056e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 3.295790465321367e+00 3.295790465311500e+00 9.86677e-12 3.24420e-11 2 -1.152328831590232e+00 -1.152328831581145e+00 9.08718e-12 4.75300e-11 3 2.994639453047198e+00 2.994639453053889e+00 6.69065e-12 3.74918e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 6.757217684182137e-01 6.757217684210876e-01 2.87381e-12 1.37781e-11 2 1.189624808769604e-01 1.189624808776735e-01 7.13055e-13 8.72223e-12 3 -5.892342102924923e-01 -5.892342102919361e-01 5.56222e-13 8.98770e-12 ----------------------------------------------------------------------------------------------------- 18 Si 1 -1.493081066237730e+00 -1.493081066251321e+00 1.35905e-11 4.38187e-11 2 -1.846863351326197e-01 -1.846863351285560e-01 4.06369e-12 1.30478e-10 3 3.122478229376963e+00 3.122478229380861e+00 3.89777e-12 6.86038e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 1.180556399249872e+00 1.180556399254998e+00 5.12590e-12 4.52243e-11 2 7.360107545968379e+00 7.360107545969962e+00 1.58273e-12 1.00362e-10 3 -4.064947543545832e+00 -4.064947543545157e+00 6.74127e-13 3.28475e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 2.817169470710407e+00 2.817169470713676e+00 3.26850e-12 3.44227e-11 2 -1.992814101379869e+00 -1.992814101378233e+00 1.63691e-12 2.30984e-11 3 2.161440523191434e-01 2.161440523265790e-01 7.43569e-12 1.16164e-10 ----------------------------------------------------------------------------------------------------- 21 Si 1 -5.386365548868540e+00 -5.386365548872010e+00 3.47011e-12 1.23506e-10 2 5.004067551945986e-02 5.004067550629358e-02 1.31663e-11 7.68954e-11 3 -1.314787518339779e+00 -1.314787518351245e+00 1.14653e-11 6.92528e-11 ----------------------------------------------------------------------------------------------------- 22 Si 1 2.710065699799043e-01 2.710065699790865e-01 8.17790e-13 1.56488e-10 2 1.791818062161683e+00 1.791818062164075e+00 2.39231e-12 2.81772e-11 3 -3.300135424407539e+00 -3.300135424395271e+00 1.22684e-11 1.99477e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 2.233295893135177e+00 2.233295893132706e+00 2.47091e-12 9.54121e-11 2 -5.968286462017766e-01 -5.968286461988025e-01 2.97407e-12 1.91039e-11 3 4.676422519126538e+00 4.676422519128429e+00 1.89093e-12 6.16014e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -1.342271719654059e+00 -1.342271719651442e+00 2.61724e-12 1.10314e-11 2 2.928182242852157e+00 2.928182242852079e+00 7.81597e-14 9.07332e-11 3 -1.461022401781177e+00 -1.461022401793901e+00 1.27243e-11 1.07505e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -1.925624580165909e+00 -1.925624580165405e+00 5.04485e-13 8.72878e-10 * 2 -3.883414680501481e+00 -3.883414680525263e+00 2.37828e-11 3.54118e-10 * 3 -5.583503401789383e+00 -5.583503401792685e+00 3.30136e-12 1.49303e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 2.218985571530465e+00 2.218985571529493e+00 9.72555e-13 8.85354e-11 2 2.252234978414685e+00 2.252234978388743e+00 2.59415e-11 1.34595e-11 3 1.510018089136489e+00 1.510018089134410e+00 2.07856e-12 1.50043e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 1.055330958851269e+01 1.055330958850736e+01 5.32374e-12 1.38584e-10 2 -4.797627971663085e+00 -4.797627971654170e+00 8.91553e-12 4.19281e-10 * 3 3.301669734269864e+00 3.301669734266228e+00 3.63620e-12 2.17706e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 5.892987610266430e-01 5.892987610260607e-01 5.82312e-13 4.29363e-11 2 -1.136527984873892e-01 -1.136527984845803e-01 2.80895e-12 3.88764e-11 3 -2.211803462035550e+00 -2.211803462041983e+00 6.43263e-12 1.33472e-10 ----------------------------------------------------------------------------------------------------- 29 Si 1 -3.821041099756698e+00 -3.821041099755371e+00 1.32649e-12 2.12806e-10 2 1.306155412388078e-02 1.306155413319635e-02 9.31557e-12 2.73161e-10 3 1.098256046051732e+00 1.098256046039929e+00 1.18026e-11 1.00890e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 -4.269495192204047e+00 -4.269495192206043e+00 1.99574e-12 8.69429e-11 2 -4.354049077667213e+00 -4.354049077666555e+00 6.58140e-13 7.31726e-11 3 -5.296044485595479e+00 -5.296044485601545e+00 6.06626e-12 2.68763e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -5.963771520031301e+00 -5.963771520024384e+00 6.91713e-12 8.03446e-11 2 5.788635906680850e-01 5.788635906613550e-01 6.73006e-12 7.37792e-11 3 6.807519159373641e-01 6.807519159209086e-01 1.64555e-11 3.65566e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.230261610424622e+00 3.230261610409877e+00 1.47451e-11 7.94462e-11 2 -2.368886675964938e+00 -2.368886675974343e+00 9.40537e-12 8.12932e-11 3 1.107116973397652e-01 1.107116973305089e-01 9.25628e-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 = ----------------------- = 7.13205e-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 -9.619583683593008e-01 1.07910e-11 1.10573e-10 2 -4.419885242518684e-01 -4.419885242494209e-01 2.44754e-12 6.41415e-12 3 -7.684395851995764e-01 -7.684395851979745e-01 1.60194e-12 1.73545e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -3.752990748118234e+00 -3.752990748131167e+00 1.29328e-11 2.69078e-10 2 4.084935012142576e+00 4.084935012136184e+00 6.39133e-12 2.07718e-11 3 -9.585554497950586e-01 -9.585554497913984e-01 3.66018e-12 3.87446e-12 ----------------------------------------------------------------------------------------------------- 3 Ge 1 1.064730834261852e+00 1.064730834257245e+00 4.60676e-12 9.86613e-11 2 -2.583897671615959e+00 -2.583897671616772e+00 8.12683e-13 4.53415e-12 3 1.248346171118795e+00 1.248346171114544e+00 4.25104e-12 2.98224e-11 ----------------------------------------------------------------------------------------------------- 4 Ge 1 8.453458264934581e-02 8.453458264050567e-02 8.84014e-12 1.54170e-11 2 1.325505130818224e+00 1.325505130855163e+00 3.69391e-11 2.09015e-10 3 5.098853263918870e-01 5.098853263890283e-01 2.85871e-12 6.52124e-11 ----------------------------------------------------------------------------------------------------- 5 Ge 1 6.174305603570173e+00 6.174305603572597e+00 2.42384e-12 8.45972e-11 2 2.061601357881707e+00 2.061601357877562e+00 4.14513e-12 2.47180e-11 3 4.033080447686298e+00 4.033080447675265e+00 1.10330e-11 8.12213e-11 ----------------------------------------------------------------------------------------------------- 6 Ge 1 -1.307320132614258e+00 -1.307320132615480e+00 1.22191e-12 2.94689e-11 2 -1.723149601481510e+00 -1.723149601484867e+00 3.35687e-12 6.59997e-11 3 3.810382486121838e-01 3.810382486027373e-01 9.44644e-12 1.70680e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -5.627032438346701e+00 -5.627032438347835e+00 1.13420e-12 2.76473e-10 2 3.995984980976269e+00 3.995984980980178e+00 3.90887e-12 2.14362e-11 3 -2.267921086344931e+00 -2.267921086345802e+00 8.71747e-13 2.30345e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 2.320741246654468e+00 2.320741246757114e+00 1.02646e-10 9.21672e-11 2 -1.617212922927009e+00 -1.617212923098033e+00 1.71024e-10 3.39358e-10 3 3.275067947495161e+00 3.275067947494485e+00 6.75460e-13 1.47001e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 2.466859390109191e+00 2.466859390108886e+00 3.05089e-13 6.38716e-11 2 -1.233992430757515e+00 -1.233992430750028e+00 7.48690e-12 4.89191e-11 3 -7.454923740805344e-02 -7.454923739862514e-02 9.42831e-12 1.54302e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 5.341120679235761e+00 5.341120679240026e+00 4.26503e-12 1.63303e-09 * 2 -4.358030611033792e+00 -4.358030611037243e+00 3.45146e-12 6.83276e-12 3 3.523003320293057e+00 3.523003320295578e+00 2.52109e-12 7.86282e-11 ----------------------------------------------------------------------------------------------------- 11 Ge 1 1.309908520080328e+00 1.309908520097767e+00 1.74389e-11 3.59519e-10 * 2 -2.087609839980404e+00 -2.087609840010785e+00 3.03801e-11 5.75204e-10 * 3 -2.111948801337255e+00 -2.111948801340668e+00 3.41283e-12 1.01616e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 2.057589011685078e-01 2.057589011677639e-01 7.43905e-13 1.29389e-11 2 -4.475728600224085e-01 -4.475728600233380e-01 9.29423e-13 4.55430e-11 3 -1.297165305633821e+00 -1.297165305630573e+00 3.24851e-12 6.57816e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -4.936313841584451e+00 -4.936313841594155e+00 9.70424e-12 1.12792e-10 2 7.126596855371838e+00 7.126596855376508e+00 4.67093e-12 1.70566e-11 3 2.169244547434653e+00 2.169244547426615e+00 8.03846e-12 1.96358e-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 -9.663275616131108e-01 1.45672e-11 5.46795e-11 2 1.618050694298244e+00 1.618050694296620e+00 1.62403e-12 2.12959e-11 3 6.465488898426823e-01 6.465488898488111e-01 6.12876e-12 4.32446e-11 ----------------------------------------------------------------------------------------------------- 16 Ge 1 -2.164014558814236e+00 -2.164014558806000e+00 8.23563e-12 4.22945e-10 * 2 -5.199576253410824e-01 -5.199576253438646e-01 2.78222e-12 5.15146e-11 3 -5.744844819571722e+00 -5.744844819569225e+00 2.49756e-12 4.54987e-11 ----------------------------------------------------------------------------------------------------- 17 Ge 1 1.237745362584834e+00 1.237745362580855e+00 3.97926e-12 1.52980e-11 2 1.273344471250780e+00 1.273344471251435e+00 6.55476e-13 5.51694e-11 3 9.872684151082424e-04 9.872684166133960e-04 1.50515e-12 1.46561e-11 ----------------------------------------------------------------------------------------------------- 18 Ge 1 -2.251386439627901e+00 -2.251386439617486e+00 1.04157e-11 4.59188e-11 2 -6.302158000506632e+00 -6.302158000510784e+00 4.15135e-12 1.14428e-10 3 -2.911093749673771e+00 -2.911093749688041e+00 1.42704e-11 3.85818e-10 * ----------------------------------------------------------------------------------------------------- 19 Si 1 6.724627228308613e-01 6.724627228145608e-01 1.63005e-11 1.46110e-11 2 1.599364762666406e+00 1.599364762679548e+00 1.31426e-11 1.24043e-11 3 -2.397497672724020e+00 -2.397497672730637e+00 6.61649e-12 8.48761e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 3.790449787606778e+00 3.790449787602022e+00 4.75575e-12 6.16112e-11 2 4.532522146621262e+00 4.532522146609153e+00 1.21085e-11 6.12275e-11 3 -2.533577238784870e+00 -2.533577238782203e+00 2.66676e-12 3.76117e-11 ----------------------------------------------------------------------------------------------------- 21 Ge 1 -7.699316830387516e-01 -7.699316830409361e-01 2.18447e-12 1.17959e-10 2 -2.669999338045209e-01 -2.669999338086405e-01 4.11965e-12 3.32374e-11 3 -5.024060986163881e-01 -5.024060986167456e-01 3.57492e-13 2.61063e-11 ----------------------------------------------------------------------------------------------------- 22 Ge 1 -4.625114380114831e-01 -4.625114380060455e-01 5.43765e-12 6.42909e-11 2 -3.296650832501850e+00 -3.296650832534167e+00 3.23168e-11 1.30846e-10 3 1.384474729283812e+00 1.384474729279654e+00 4.15823e-12 6.86475e-11 ----------------------------------------------------------------------------------------------------- 23 Ge 1 1.050604163591629e+00 1.050604163591976e+00 3.46390e-13 1.93283e-11 2 1.247506586460626e+00 1.247506586482856e+00 2.22298e-11 9.39915e-11 3 -6.760980170192226e-01 -6.760980170238976e-01 4.67504e-12 1.37916e-10 ----------------------------------------------------------------------------------------------------- 24 Ge 1 3.348394751670194e+00 3.348394751718816e+00 4.86229e-11 9.58815e-11 2 3.731736934480860e+00 3.731736934753558e+00 2.72698e-10 6.76485e-10 * 3 5.418270111446246e-01 5.418270111439999e-01 6.24722e-13 8.62030e-11 ----------------------------------------------------------------------------------------------------- 25 Ge 1 -3.761373846233127e+00 -3.761373846227575e+00 5.55156e-12 4.44049e-11 2 -1.140788258055740e+00 -1.140788258049171e+00 6.56830e-12 1.26428e-10 3 1.876945022817374e+00 1.876945022804841e+00 1.25324e-11 1.07107e-10 ----------------------------------------------------------------------------------------------------- 26 Ge 1 6.817270217723317e-01 6.817270217716561e-01 6.75571e-13 4.70856e-11 2 2.633557875670104e+00 2.633557875668345e+00 1.75948e-12 1.50004e-11 3 2.675748703919659e-02 2.675748703876201e-02 4.34579e-13 1.10255e-11 ----------------------------------------------------------------------------------------------------- 27 Si 1 -1.755468165466379e+00 -1.755468165197312e+00 2.69067e-10 5.87013e-10 * 2 2.030127605035938e+00 2.030127605021482e+00 1.44560e-11 6.04911e-10 * 3 6.716518309642331e+00 6.716518309657849e+00 1.55183e-11 8.11493e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 9.778784535891398e-01 9.778784535850020e-01 4.13780e-12 2.92864e-11 2 -2.715121046629529e+00 -2.715121046639859e+00 1.03304e-11 7.52065e-11 3 -1.504061663586100e+00 -1.504061663585781e+00 3.19744e-13 9.44091e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 6.199115770322010e-01 6.199115770160614e-01 1.61396e-11 3.15463e-11 2 -1.843086275804246e+00 -1.843086275807341e+00 3.09530e-12 8.44897e-11 3 6.045487947340582e-01 6.045487947595679e-01 2.55097e-11 1.28273e-10 ----------------------------------------------------------------------------------------------------- 30 Si 1 1.450744634198010e+00 1.450744634193734e+00 4.27547e-12 9.04368e-11 2 -2.054728198572494e+00 -2.054728198577670e+00 5.17630e-12 9.84017e-11 3 -2.627277880684672e+00 -2.627277880675073e+00 9.59943e-12 7.59259e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -2.760688544864274e+00 -2.760688544882058e+00 1.77836e-11 1.44415e-10 2 -2.800369818105775e+00 -2.800369818103289e+00 2.48557e-12 3.98956e-11 3 -5.030596116340874e-01 -5.030596116333325e-01 7.54952e-13 8.91170e-11 ----------------------------------------------------------------------------------------------------- 32 Ge 1 -1.320560465917175e+00 -1.320560465919087e+00 1.91225e-12 2.46145e-10 2 -1.827519962282491e+00 -1.827519962306464e+00 2.39733e-11 5.69700e-11 3 -5.977730393767927e-02 -5.977730393493619e-02 2.74308e-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 = 9.14340e-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 9.14340e-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.