!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_SiII_CSi__MO_408791041969_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 4.656004944765122e+00 4.656004944763904e+00 1.21769e-12 1.86784e-11 2 2.245485921321094e+00 2.245485921311493e+00 9.60121e-12 9.30305e-11 3 4.843987397185566e+00 4.843987397188908e+00 3.34222e-12 1.86784e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -3.240984812291462e+00 -3.240984812286992e+00 4.46931e-12 4.19309e-11 2 1.868060167107362e+00 1.868060167101436e+00 5.92593e-12 2.80453e-11 3 -4.898658544163931e-02 -4.898658543612325e-02 5.51606e-12 9.11657e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 6.849838494466502e+00 6.849838494464605e+00 1.89626e-12 1.69251e-11 2 -6.267667714674809e+00 -6.267667714667160e+00 7.64899e-12 3.51514e-11 3 -7.231110654084022e+00 -7.231110654089517e+00 5.49516e-12 8.53930e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 -3.683460472083390e+00 -3.683460472088572e+00 5.18208e-12 5.97504e-11 2 1.210404907304018e+01 1.210404907304210e+01 1.92379e-12 2.14175e-11 3 -6.047482337619459e+00 -6.047482337618011e+00 1.44773e-12 1.09486e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -1.925286484887357e+00 -1.925286484886642e+00 7.14762e-13 1.62652e-11 2 1.834328138772098e+00 1.834328138767815e+00 4.28280e-12 1.30107e-11 3 2.293878323168971e+00 2.293878323151037e+00 1.79332e-11 1.56072e-10 ----------------------------------------------------------------------------------------------------- 6 C 1 -1.355828222078300e+00 -1.355828222082583e+00 4.28346e-12 6.40263e-11 2 -4.001382588039466e+00 -4.001382588035790e+00 3.67617e-12 1.78186e-11 3 1.306964931018425e+00 1.306964931018822e+00 3.97238e-13 9.20264e-12 ----------------------------------------------------------------------------------------------------- 7 C 1 -1.667098069537463e+00 -1.667098069533466e+00 3.99636e-12 6.21347e-12 2 -6.181506392895456e+00 -6.181506392894025e+00 1.43086e-12 3.88418e-11 3 -1.257192100141992e+01 -1.257192100142717e+01 7.25286e-12 2.78231e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 -2.637829128386464e+00 -2.637829128383606e+00 2.85816e-12 5.82512e-11 2 2.631332197163502e+00 2.631332197165753e+00 2.25109e-12 3.68310e-11 3 6.333157814682740e+00 6.333157814678958e+00 3.78186e-12 1.97217e-10 * ----------------------------------------------------------------------------------------------------- 9 C 1 -1.079354480439393e+00 -1.079354480446490e+00 7.09677e-12 2.11684e-10 * 2 -3.745731390933440e+00 -3.745731390923654e+00 9.78551e-12 1.33755e-11 3 3.046883312422022e+00 3.046883312424694e+00 2.67253e-12 4.57345e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 -4.029410761140491e+00 -4.029410761143010e+00 2.51976e-12 5.18900e-11 2 8.804346810007613e-01 8.804346810089229e-01 8.16158e-12 8.00893e-12 3 -2.429547835823549e+00 -2.429547835818084e+00 5.46496e-12 9.81792e-12 ----------------------------------------------------------------------------------------------------- 11 C 1 -6.608884377862515e-01 -6.608884377920980e-01 5.84655e-12 2.24345e-11 2 -1.377065127701543e+01 -1.377065127701419e+01 1.23634e-12 3.58895e-11 3 -6.283995277341145e+00 -6.283995277332536e+00 8.60911e-12 3.96012e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 -1.540049442890757e+00 -1.540049442882564e+00 8.19278e-12 1.90270e-11 2 1.772488490264885e+00 1.772488490274211e+00 9.32587e-12 3.23028e-11 3 -5.216682297189716e-01 -5.216682297187065e-01 2.65121e-13 2.14747e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 -4.240427330197039e+00 -4.240427330199457e+00 2.41762e-12 1.68114e-11 2 -3.118823716369271e+00 -3.118823716373096e+00 3.82494e-12 3.60987e-11 3 -1.153084437032416e+01 -1.153084437032448e+01 3.14415e-13 2.03535e-11 ----------------------------------------------------------------------------------------------------- 14 C 1 2.708129400578050e+00 2.708129400581595e+00 3.54472e-12 3.87970e-11 2 2.873778376681987e-01 2.873778376697572e-01 1.55842e-12 8.82822e-12 3 -2.292413285601308e+00 -2.292413285601988e+00 6.80345e-13 1.17817e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 1.053410691836803e+01 1.053410691837062e+01 2.59170e-12 1.01199e-11 2 2.167899291247959e+00 2.167899291246700e+00 1.25944e-12 7.77867e-11 3 4.940953642373962e+00 4.940953642370800e+00 3.16192e-12 2.07319e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 -5.824188705067430e-01 -5.824188705008883e-01 5.85476e-12 4.36132e-11 2 7.358126409712471e+00 7.358126409711236e+00 1.23457e-12 2.57394e-11 3 4.216431050372703e+00 4.216431050370400e+00 2.30305e-12 2.56561e-10 * ----------------------------------------------------------------------------------------------------- 17 C 1 -6.300009134354815e+00 -6.300009134354957e+00 1.42109e-13 1.48441e-11 2 -2.916541767976833e+00 -2.916541767974131e+00 2.70273e-12 1.74847e-11 3 -1.840539143841227e+00 -1.840539143850157e+00 8.93019e-12 5.51170e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 2.499477896161990e+00 2.499477896161156e+00 8.34000e-13 8.54334e-11 2 7.084495241498399e+00 7.084495241490471e+00 7.92877e-12 2.39710e-11 3 -4.095641831394464e+00 -4.095641831399793e+00 5.32907e-12 1.25882e-11 ----------------------------------------------------------------------------------------------------- 19 C 1 1.014959298188851e+01 1.014959298190815e+01 1.96447e-11 3.08535e-11 2 -2.867380337243860e+00 -2.867380337242596e+00 1.26388e-12 1.16942e-11 3 3.205197049214294e+00 3.205197049214265e+00 2.88658e-14 5.90399e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 -7.208306142101408e-01 -7.208306142108447e-01 7.03881e-13 9.84812e-12 2 9.032337972215347e-01 9.032337972205191e-01 1.01563e-12 1.59130e-11 3 1.138470390045028e+00 1.138470390044076e+00 9.51239e-13 5.68701e-12 ----------------------------------------------------------------------------------------------------- 21 C 1 -6.326196079661608e+00 -6.326196079667544e+00 5.93570e-12 1.18676e-10 2 -3.571465349841367e+00 -3.571465349832169e+00 9.19798e-12 1.18940e-11 3 6.759809582273732e+00 6.759809582268161e+00 5.57066e-12 7.92433e-11 ----------------------------------------------------------------------------------------------------- 22 C 1 3.419649484270094e+00 3.419649484271207e+00 1.11333e-12 1.31504e-11 2 4.422919124861641e+00 4.422919124856020e+00 5.62128e-12 2.87974e-11 3 9.307033357149335e+00 9.307033357141155e+00 8.18012e-12 4.15668e-12 ----------------------------------------------------------------------------------------------------- 23 C 1 -2.822378860357555e+00 -2.822378860357823e+00 2.67786e-13 1.62812e-11 2 2.547541596473605e+00 2.547541596472940e+00 6.64802e-13 2.26006e-11 3 -2.454115222441570e+00 -2.454115222443287e+00 1.71640e-12 1.75486e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 6.927772877420231e+00 6.927772877426276e+00 6.04494e-12 3.07034e-11 2 5.095731465728502e+00 5.095731465733639e+00 5.13722e-12 1.53015e-11 3 -1.530458008713220e+00 -1.530458008718977e+00 5.75673e-12 5.21587e-11 ----------------------------------------------------------------------------------------------------- 25 C 1 -2.445581566713729e-01 -2.445581566832986e-01 1.19257e-11 5.58032e-11 2 -4.068959095094306e+00 -4.068959095085452e+00 8.85425e-12 5.92344e-11 3 -2.110905217132644e+00 -2.110905217128577e+00 4.06697e-12 3.59535e-12 ----------------------------------------------------------------------------------------------------- 26 C 1 -1.025267977761835e+00 -1.025267977757663e+00 4.17244e-12 1.27299e-10 2 4.717767568281101e+00 4.717767568266297e+00 1.48042e-11 1.68525e-10 * 3 2.231962628533338e+00 2.231962628522562e+00 1.07763e-11 2.43952e-11 ----------------------------------------------------------------------------------------------------- 27 C 1 5.836290926580632e+00 5.836290926581830e+00 1.19815e-12 1.75646e-11 2 -4.810953074594795e+00 -4.810953074595729e+00 9.34364e-13 5.59872e-11 3 2.803414093307876e+00 2.803414093299136e+00 8.74012e-12 4.71978e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -7.394668445152030e+00 -7.394668445153492e+00 1.46194e-12 1.39302e-11 2 5.593176192284728e+00 5.593176192284496e+00 2.31815e-13 1.03570e-11 3 3.012358348703033e-01 3.012358348710886e-01 7.85372e-13 3.44408e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 7.590992499428726e-01 7.590992499423830e-01 4.89608e-13 1.46606e-11 2 -4.767615593042215e+00 -4.767615593041216e+00 9.99201e-13 8.92886e-12 3 -1.215616171167717e+00 -1.215616171173000e+00 5.28222e-12 2.14808e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 1.996115213028611e+00 1.996115213008048e+00 2.05624e-11 3.41069e-11 2 2.719438101722380e-01 2.719438101749148e-01 2.67686e-12 1.97808e-11 3 -1.247642294790025e+00 -1.247642294792265e+00 2.24043e-12 2.40712e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 -5.610523981277987e+00 -5.610523981280751e+00 2.76401e-12 9.03517e-11 2 -5.323819855392009e+00 -5.323819855389135e+00 2.87415e-12 5.22808e-11 3 5.451881928453830e+00 5.451881928457683e+00 3.85292e-12 1.94813e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 7.513913742018093e-01 7.513913741951304e-01 6.67899e-12 2.62622e-11 2 1.626107149293014e+00 1.626107149292035e+00 9.79439e-13 4.78242e-11 3 5.271626131782917e+00 5.271626131783363e+00 4.46754e-13 2.81188e-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 = 2, direction = 3: |F_model - F_numer| error = --------------------------------- = 1.12603e-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 = 3.94382762909 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 8.332300306712904e+00 8.332300306717029e+00 4.12470e-12 4.36753e-11 2 3.383027402234663e+00 3.383027402239714e+00 5.05107e-12 3.78937e-11 3 4.268961983424753e+00 4.268961983415942e+00 8.81073e-12 1.82299e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 -4.859563744433893e+00 -4.859563744433441e+00 4.52083e-13 1.93614e-11 2 1.711920267860769e+00 1.711920267860032e+00 7.37410e-13 4.17892e-11 3 7.165110293627952e-01 7.165110293640682e-01 1.27298e-12 2.14184e-12 ----------------------------------------------------------------------------------------------------- 3 Si 1 -2.603897859518673e+00 -2.603897859516552e+00 2.12097e-12 2.96390e-11 2 1.501808785799840e+00 1.501808785798693e+00 1.14664e-12 1.88749e-11 3 -3.318876231294974e+00 -3.318876231299706e+00 4.73133e-12 7.81553e-12 ----------------------------------------------------------------------------------------------------- 4 Si 1 5.688976198710216e+00 5.688976198710703e+00 4.87610e-13 5.97353e-11 2 -3.591635640295632e-01 -3.591635640279772e-01 1.58601e-12 1.19146e-11 3 5.774999889952666e+00 5.774999889953684e+00 1.01874e-12 1.88507e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 4.508812711072041e+00 4.508812711069305e+00 2.73648e-12 3.29026e-11 2 4.425713676194025e+00 4.425713676189372e+00 4.65317e-12 2.87859e-12 3 6.662441711660125e+00 6.662441711669573e+00 9.44844e-12 5.69562e-11 ----------------------------------------------------------------------------------------------------- 6 Si 1 -4.659476567807827e+00 -4.659476567809303e+00 1.47615e-12 3.36300e-11 2 -2.197002697837228e+00 -2.197002697833360e+00 3.86846e-12 8.72724e-12 3 4.077733294260617e+00 4.077733294266323e+00 5.70566e-12 8.40661e-12 ----------------------------------------------------------------------------------------------------- 7 Si 1 -3.548690069388198e+00 -3.548690069382882e+00 5.31664e-12 2.66129e-11 2 4.273105132918938e+00 4.273105132920415e+00 1.47704e-12 5.16733e-11 3 -1.275923148417806e+00 -1.275923148423674e+00 5.86797e-12 7.72651e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -4.114499023652677e-01 -4.114499023695206e-01 4.25293e-12 3.24322e-11 2 8.022072225396175e-01 8.022072225444384e-01 4.82092e-12 7.51840e-11 3 -3.101788186626937e+00 -3.101788186628452e+00 1.51523e-12 3.89448e-11 ----------------------------------------------------------------------------------------------------- 9 Si 1 4.907131047026932e+00 4.907131047026190e+00 7.42517e-13 1.04574e-11 2 -4.203469729587160e+00 -4.203469729587384e+00 2.23821e-13 4.43032e-11 3 1.924365497192250e+00 1.924365497197539e+00 5.28910e-12 1.02464e-10 ----------------------------------------------------------------------------------------------------- 10 Si 1 1.312718947870921e+00 1.312718947871415e+00 4.94715e-13 5.98890e-11 2 -2.751730884771873e+00 -2.751730884771085e+00 7.87814e-13 1.50413e-10 3 6.493609975377200e+00 6.493609975377452e+00 2.52243e-13 6.00702e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -5.809176330664108e+00 -5.809176330677824e+00 1.37153e-11 3.63629e-11 2 2.334405695934366e+00 2.334405695922746e+00 1.16192e-11 7.33995e-11 3 -9.404754769534636e-01 -9.404754769472966e-01 6.16696e-12 4.58217e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 5.298250560744181e+00 5.298250560742582e+00 1.59872e-12 2.36717e-11 2 -4.286291928624339e+00 -4.286291928625523e+00 1.18483e-12 7.17826e-12 3 -1.542271117918098e+00 -1.542271117909682e+00 8.41616e-12 1.43836e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -6.899219558039234e+00 -6.899219558041274e+00 2.04015e-12 4.94982e-11 2 -7.614018467409888e-01 -7.614018467436773e-01 2.68852e-12 2.19283e-11 3 -9.409867612504885e-01 -9.409867612505274e-01 3.88578e-14 5.48429e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 -1.629295922681666e+00 -1.629295922679819e+00 1.84697e-12 4.81395e-11 2 -9.236120287482336e-01 -9.236120287457159e-01 2.51765e-12 1.34990e-11 3 1.632260081187727e+00 1.632260081185834e+00 1.89337e-12 9.29905e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 1.445007564902956e+00 1.445007564906781e+00 3.82494e-12 8.96527e-12 2 -7.872693715169552e-01 -7.872693715017929e-01 1.51623e-11 1.74430e-11 3 4.097208949199815e+00 4.097208949203126e+00 3.31113e-12 5.33760e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 -1.222648495232863e+00 -1.222648495242221e+00 9.35807e-12 5.56122e-11 2 -2.192840453344817e+00 -2.192840453352978e+00 8.16058e-12 2.84932e-11 3 -2.509578380616035e+00 -2.509578380598770e+00 1.72653e-11 9.02611e-12 ----------------------------------------------------------------------------------------------------- 17 Si 1 4.131198686670070e+00 4.131198686669768e+00 3.01981e-13 5.84803e-11 2 4.776763793867628e+00 4.776763793855407e+00 1.22204e-11 3.00311e-11 3 -2.247582344055527e+00 -2.247582344059534e+00 4.00657e-12 4.38658e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 -5.247159064242651e+00 -5.247159064251218e+00 8.56648e-12 2.20606e-11 2 1.621672206562313e-01 1.621672206578326e-01 1.60130e-12 1.36886e-10 3 3.271672788115625e-01 3.271672787931998e-01 1.83626e-11 1.96431e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 -3.843791488084961e+00 -3.843791488086512e+00 1.55165e-12 1.57168e-11 2 -1.418068036050410e+00 -1.418068036048300e+00 2.11076e-12 1.66332e-10 3 -3.239175764190334e+00 -3.239175764192635e+00 2.30083e-12 4.52520e-10 * ----------------------------------------------------------------------------------------------------- 20 Si 1 3.844032753390155e+00 3.844032753394931e+00 4.77574e-12 6.24976e-11 2 3.900201874017704e+00 3.900201874022010e+00 4.30633e-12 3.01159e-11 3 -3.866423621181492e+00 -3.866423621187355e+00 5.86287e-12 4.63527e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 1.520061737018516e+00 1.520061737016207e+00 2.30860e-12 1.51070e-10 2 3.079775866231842e+00 3.079775866220787e+00 1.10547e-11 1.86873e-11 3 2.331320421913321e+00 2.331320421920133e+00 6.81277e-12 3.79822e-10 * ----------------------------------------------------------------------------------------------------- 22 Si 1 1.146742061536409e-02 1.146742060444941e-02 1.09147e-11 7.51352e-11 2 -5.522011362165467e+00 -5.522011362154585e+00 1.08829e-11 1.25044e-10 3 2.269521902545290e+00 2.269521902546149e+00 8.58869e-13 2.28870e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -3.335011293229809e+00 -3.335011293221005e+00 8.80318e-12 5.33840e-12 2 4.679529398241519e+00 4.679529398239504e+00 2.01528e-12 9.66249e-12 3 -6.410848899190078e+00 -6.410848899194357e+00 4.27836e-12 2.62164e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 1.448975466180425e+00 1.448975466185349e+00 4.92451e-12 2.91900e-11 2 5.203431514806875e+00 5.203431514797929e+00 8.94662e-12 2.63229e-11 3 -2.644819569608846e+00 -2.644819569605796e+00 3.05000e-12 3.38383e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 4.690243963006170e+00 4.690243963006523e+00 3.53495e-13 1.29383e-10 2 -1.804887401481622e+00 -1.804887401488932e+00 7.30971e-12 4.44158e-11 3 -4.644115881374308e-01 -4.644115881391964e-01 1.76553e-12 4.20929e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 -2.471699668676119e+00 -2.471699668671916e+00 4.20330e-12 1.70934e-11 2 -8.571631134033170e-01 -8.571631134065432e-01 3.22620e-12 5.08326e-11 3 3.202953813426872e+00 3.202953813423331e+00 3.54161e-12 1.10710e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 -3.450045472299997e+00 -3.450045472290706e+00 9.29079e-12 1.71076e-10 2 -1.060010067048176e+00 -1.060010067051273e+00 3.09708e-12 9.64242e-11 3 -4.702352952800665e+00 -4.702352952797164e+00 3.50120e-12 4.53770e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 5.959567932296094e+00 5.959567932293628e+00 2.46647e-12 1.57687e-11 2 -3.936568216525596e+00 -3.936568216526981e+00 1.38423e-12 2.19695e-09 * 3 -2.275336049133410e+00 -2.275336049130080e+00 3.33067e-12 4.21805e-11 ----------------------------------------------------------------------------------------------------- 29 Si 1 3.497743601012599e+00 3.497743601009907e+00 2.69162e-12 5.10627e-11 2 1.314167644235541e+00 1.314167644227392e+00 8.14948e-12 3.18408e-11 3 6.520168962771380e-01 6.520168962731822e-01 3.95584e-12 2.34829e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 -3.143197119565218e+00 -3.143197119566172e+00 9.53460e-13 2.66764e-11 2 -3.941839890247316e+00 -3.941839890261995e+00 1.46789e-11 5.47543e-10 * 3 -1.974662749677991e+00 -1.974662749697652e+00 1.96607e-11 2.34934e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -3.893306510549376e+00 -3.893306510547657e+00 1.71907e-12 2.43170e-10 * 2 -1.820523847972761e+00 -1.820523847969819e+00 2.94209e-12 5.76135e-11 3 -1.480889010728037e+00 -1.480889010725456e+00 2.58105e-12 4.14082e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 4.311401695503239e-01 4.311401695595260e-01 9.20208e-12 4.08520e-11 2 -2.724371055443740e+00 -2.724371055450332e+00 6.59206e-12 1.09961e-11 3 -1.494670872810509e+00 -1.494670872808476e+00 2.03304e-12 6.27716e-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 = 22, direction = 1: |F_model - F_numer| error = --------------------------------- = 9.51799e-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. MIXED STRUCTURE -- Species = C Si | a0 = 3.25692165969 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 1.726513464049515e+00 1.726513464163494e+00 1.13979e-10 1.93635e-09 2 -1.434837270221273e+00 -1.434837271121894e+00 9.00622e-10 6.56175e-09 3 1.118959855504624e+00 1.118959855440654e+00 6.39695e-11 1.22335e-09 ----------------------------------------------------------------------------------------------------- 2 C 1 8.908375019302332e+00 8.908375019005071e+00 2.97261e-10 1.34136e-08 2 -8.707953401810084e+00 -8.707953408332079e+00 6.52200e-09 8.75628e-09 3 -1.164232005307768e+00 -1.164232006180852e+00 8.73084e-10 8.05484e-09 ----------------------------------------------------------------------------------------------------- 3 C 1 -3.349576275242390e-01 -3.349576271803002e-01 3.43939e-10 1.03482e-08 2 -1.270973858695219e+00 -1.270973859087136e+00 3.91917e-10 8.45887e-09 3 -1.025787816042016e-01 -1.025787830377817e-01 1.43358e-09 6.99939e-09 ----------------------------------------------------------------------------------------------------- 4 Si 1 -8.055689154305632e+00 -8.055689154453319e+00 1.47686e-10 3.22204e-09 2 -6.870429398027588e+00 -6.870429399466846e+00 1.43926e-09 1.58409e-07 * 3 4.079944029478028e+00 4.079944029223941e+00 2.54087e-10 4.29045e-09 ----------------------------------------------------------------------------------------------------- 5 Si 1 -1.446029096604573e+01 -1.446029096526365e+01 7.82075e-10 1.06204e-06 * 2 -8.788491342948733e+00 -8.788491343287440e+00 3.38707e-10 2.31874e-07 * 3 -1.518804891904626e-01 -1.518804888457672e-01 3.44695e-10 2.45739e-08 ----------------------------------------------------------------------------------------------------- 6 Si 1 1.459423545355798e+01 1.459423545323477e+01 3.23217e-10 8.75670e-09 2 7.282465642250490e+00 7.282465641781074e+00 4.69417e-10 1.12082e-08 3 -9.228080464961477e-01 -9.228080457407994e-01 7.55348e-10 2.08666e-09 ----------------------------------------------------------------------------------------------------- 7 C 1 -1.041894030512021e+00 -1.041894030323481e+00 1.88540e-10 8.23901e-09 2 3.364846850268770e+00 3.364846851024351e+00 7.55582e-10 6.85748e-09 3 1.395773389421927e+00 1.395773389831358e+00 4.09431e-10 6.57526e-08 * ----------------------------------------------------------------------------------------------------- 8 C 1 -2.016809620735648e+00 -2.016809622657490e+00 1.92184e-09 5.01257e-09 2 -7.536057495550628e+00 -7.536057491971063e+00 3.57957e-09 6.41887e-09 3 -1.737313090810487e+00 -1.737313095628853e+00 4.81837e-09 3.83470e-08 * ----------------------------------------------------------------------------------------------------- 9 C 1 -6.397011775382310e+00 -6.397011775932174e+00 5.49863e-10 3.03852e-08 * 2 1.181066202195510e+01 1.181066202148157e+01 4.73523e-10 1.14981e-08 3 -1.670034929924369e+00 -1.670034929966406e+00 4.20377e-11 4.15209e-09 ----------------------------------------------------------------------------------------------------- 10 C 1 1.346662838450894e-01 1.346662839908842e-01 1.45795e-10 1.93451e-09 2 2.222952670732229e+00 2.222952669673008e+00 1.05922e-09 1.50212e-09 3 1.728537780759437e+00 1.728537780020482e+00 7.38956e-10 3.31674e-09 ----------------------------------------------------------------------------------------------------- 11 Si 1 2.071717784072626e+00 2.071717785339438e+00 1.26681e-09 2.28529e-09 2 -7.133765574113498e+00 -7.133765572328739e+00 1.78476e-09 5.35990e-09 3 2.889320988811107e+00 2.889320992258478e+00 3.44737e-09 2.02007e-08 ----------------------------------------------------------------------------------------------------- 12 Si 1 1.317575485186713e+00 1.317575485238197e+00 5.14848e-11 5.75659e-09 2 -2.543031473563468e+00 -2.543031473136317e+00 4.27152e-10 2.61237e-09 3 -1.738703552458675e+00 -1.738703551558418e+00 9.00257e-10 9.68349e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -9.540519300704062e+00 -9.540519299961145e+00 7.42917e-10 3.29218e-09 2 1.300788722317240e+00 1.300788721852031e+00 4.65209e-10 8.32062e-08 * 3 -1.534469398246403e+01 -1.534469398306815e+01 6.04118e-10 2.21729e-09 ----------------------------------------------------------------------------------------------------- 14 Si 1 8.409309679249979e+00 8.409309678328757e+00 9.21222e-10 5.22910e-09 2 5.229761750072851e+00 5.229761751183127e+00 1.11028e-09 2.67783e-09 3 -8.958884817749723e+00 -8.958884818533106e+00 7.83382e-10 3.39474e-09 ----------------------------------------------------------------------------------------------------- 15 C 1 4.642948813016598e+00 4.642948814856435e+00 1.83984e-09 2.54890e-08 2 1.656858285684093e+00 1.656858285245563e+00 4.38530e-10 1.11062e-08 3 1.407251071383019e+01 1.407251071375764e+01 7.25464e-11 4.79980e-09 ----------------------------------------------------------------------------------------------------- 16 Si 1 1.396590144482356e+00 1.396590143763974e+00 7.18382e-10 3.59356e-09 2 1.046976393382183e+01 1.046976393128965e+01 2.53218e-09 3.55758e-09 3 2.552026986289459e+00 2.552026986859015e+00 5.69556e-10 2.04479e-09 ----------------------------------------------------------------------------------------------------- 17 Si 1 -1.755027948212905e+00 -1.755027947458381e+00 7.54524e-10 4.95856e-09 2 -4.017293363049278e+00 -4.017293363585587e+00 5.36309e-10 8.35470e-10 3 3.609320033479105e-01 3.609320017637023e-01 1.58421e-09 4.08677e-09 ----------------------------------------------------------------------------------------------------- 18 C 1 3.962183166695322e+00 3.962183164226911e+00 2.46841e-09 1.25824e-08 2 2.417826795020867e+00 2.417826794358473e+00 6.62394e-10 1.29738e-08 3 -2.013058731390332e+00 -2.013058732170492e+00 7.80160e-10 4.68099e-09 ----------------------------------------------------------------------------------------------------- 19 Si 1 -6.790544027103397e+00 -6.790544027714934e+00 6.11537e-10 8.71254e-09 2 -4.113368542790388e+00 -4.113368545446199e+00 2.65581e-09 1.77307e-09 3 1.094165094563713e+00 1.094165093426381e+00 1.13733e-09 7.84556e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 -3.059984648046141e-01 -3.059984655507210e-01 7.46107e-10 5.91445e-09 2 2.939523774695008e+00 2.939523774245865e+00 4.49144e-10 2.87021e-09 3 -2.259139455260530e+00 -2.259139455619492e+00 3.58962e-10 6.64095e-09 ----------------------------------------------------------------------------------------------------- 21 C 1 -1.764483650386796e+00 -1.764483650909026e+00 5.22230e-10 2.69399e-09 2 -1.648291837854249e+00 -1.648291839836341e+00 1.98209e-09 2.95093e-09 3 -1.667059606693067e+00 -1.667059604555262e+00 2.13780e-09 2.15282e-09 ----------------------------------------------------------------------------------------------------- 22 Si 1 2.452651262835583e+00 2.452651262716620e+00 1.18963e-10 4.82836e-09 2 5.980236076925224e+00 5.980236077732952e+00 8.07728e-10 4.98958e-09 3 -6.159093598464632e+00 -6.159093598187366e+00 2.77266e-10 9.73735e-08 * ----------------------------------------------------------------------------------------------------- 23 Si 1 2.770191964553539e+00 2.770191964210616e+00 3.42923e-10 1.52108e-09 2 -1.136276808029706e+01 -1.136276808073464e+01 4.37586e-10 3.15399e-09 3 3.141289444952829e+00 3.141289444681920e+00 2.70909e-10 2.57423e-10 ----------------------------------------------------------------------------------------------------- 24 Si 1 -1.689936128893309e-02 -1.689936121595289e-02 7.29802e-11 7.40887e-09 2 8.086776762788707e+00 8.086776763797820e+00 1.00911e-09 2.10896e-09 3 5.009598749916409e+00 5.009598749620280e+00 2.96128e-10 2.25000e-09 ----------------------------------------------------------------------------------------------------- 25 C 1 -3.333775005024402e+00 -3.333775005956995e+00 9.32593e-10 9.93298e-09 2 -3.412244653093377e+00 -3.412244653699542e+00 6.06165e-10 4.22065e-09 3 2.472797336990019e-01 2.472797332147718e-01 4.84230e-10 1.01353e-09 ----------------------------------------------------------------------------------------------------- 26 C 1 -8.074714712268236e-01 -8.074714736255327e-01 2.39871e-09 4.88801e-09 2 1.834169787718428e+00 1.834169785877243e+00 1.84118e-09 2.75505e-09 3 -1.567627483251406e+00 -1.567627483645518e+00 3.94112e-10 7.17047e-09 ----------------------------------------------------------------------------------------------------- 27 Si 1 1.350687737734579e+01 1.350687737808077e+01 7.34975e-10 7.84793e-10 2 -1.578026073629257e+00 -1.578026072860169e+00 7.69088e-10 5.55604e-09 3 2.913933136700684e+00 2.913933136063440e+00 6.37244e-10 4.03401e-09 ----------------------------------------------------------------------------------------------------- 28 Si 1 -8.453121628880092e+00 -8.453121628875934e+00 4.15845e-12 2.74081e-09 2 7.073485894674020e+00 7.073485894672465e+00 1.55520e-12 4.58544e-10 3 -4.196638576270530e-01 -4.196638591535843e-01 1.52653e-09 1.52082e-09 ----------------------------------------------------------------------------------------------------- 29 C 1 5.416591454778136e+00 5.416591453996313e+00 7.81823e-10 9.88397e-09 2 4.834679050682820e+00 4.834679049135483e+00 1.54734e-09 4.22946e-08 * 3 9.953616335932162e+00 9.953616337628764e+00 1.69660e-09 1.38779e-06 * ----------------------------------------------------------------------------------------------------- 30 C 1 -1.877572328274176e+00 -1.877572328340402e+00 6.62264e-11 1.53499e-09 2 -8.173846483776707e+00 -8.173846482538332e+00 1.23837e-09 1.28814e-09 3 2.744135651583258e+00 2.744135651197891e+00 3.85367e-10 3.62226e-09 ----------------------------------------------------------------------------------------------------- 31 C 1 -7.728369957668781e+00 -7.728369957744849e+00 7.60680e-11 1.56341e-10 2 1.102914092680146e+01 1.102914092675505e+01 4.64073e-11 4.90957e-10 3 -6.208541154715803e+00 -6.208541154956650e+00 2.40846e-10 3.61339e-10 ----------------------------------------------------------------------------------------------------- 32 C 1 3.370008965109024e+00 3.370008964281128e+00 8.27896e-10 1.36308e-09 2 -8.942560096988336e+00 -8.942560097250398e+00 2.62062e-10 1.36645e-09 3 -1.216710311382055e+00 -1.216710309755734e+00 1.62632e-09 4.66115e-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 = 3, direction = 3: |F_model - F_numer| error = --------------------------------- = 1.39754e-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 = 1.39754e-08 Machine precision = 2.22045e-16 Grade: B Comment: The letter grade B was assigned because the normalized error in the computation was 1.39754e-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.