!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Sim_LAMMPS_TersoffZBL_DevanathanDiazdelaRubiaWeber_1998_SiC__SM_578912636995_000 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 = 2.7171401977539062 | (Configuration in file "config-C.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 C 1 1.010238665938262e+01 1.010238665938089e+01 1.72129e-12 8.96403e-11 2 3.803722850162645e+00 3.803722850161195e+00 1.44995e-12 1.07439e-11 3 6.953136947582919e+00 6.953136947584478e+00 1.55964e-12 1.11138e-11 ----------------------------------------------------------------------------------------------------- 2 C 1 -4.706126646379500e+00 -4.706126646393262e+00 1.37614e-11 2.98472e-11 2 1.746002703117288e-01 1.746002703085175e-01 3.21132e-12 3.75101e-11 3 7.057479782509919e-01 7.057479782517602e-01 7.68274e-13 8.48825e-11 ----------------------------------------------------------------------------------------------------- 3 C 1 -2.769945989993387e+00 -2.769945989976605e+00 1.67826e-11 1.08516e-10 2 -2.287204044911517e+00 -2.287204044902372e+00 9.14513e-12 5.31100e-11 3 -9.026478074236643e+00 -9.026478074224148e+00 1.24949e-11 2.54836e-11 ----------------------------------------------------------------------------------------------------- 4 C 1 4.098757887896826e+00 4.098757887891130e+00 5.69589e-12 8.04112e-11 2 8.463013329828422e+00 8.463013329822997e+00 5.42499e-12 1.43453e-10 3 -9.076891956385771e-01 -9.076891956362559e-01 2.32114e-12 6.67328e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 8.925879376534998e-01 8.925879376542706e-01 7.70828e-13 6.74168e-11 2 -2.654480885910989e-01 -2.654480885892091e-01 1.88982e-12 1.19694e-10 3 4.572898658641168e+00 4.572898658646745e+00 5.57687e-12 6.89298e-11 ----------------------------------------------------------------------------------------------------- 6 C 1 -9.339776787915575e-01 -9.339776787954676e-01 3.91009e-12 5.91814e-11 2 -5.261565383724094e+00 -5.261565383726649e+00 2.55440e-12 1.84208e-11 3 8.316867337195600e+00 8.316867337194552e+00 1.04805e-12 6.82334e-11 ----------------------------------------------------------------------------------------------------- 7 C 1 2.194024871565228e-01 2.194024871767924e-01 2.02697e-11 2.25055e-11 2 -4.029007514056886e+00 -4.029007514060887e+00 4.00124e-12 1.41087e-11 3 -2.114989183836604e+01 -2.114989183836389e+01 2.14939e-12 7.01590e-11 ----------------------------------------------------------------------------------------------------- 8 C 1 -6.657201481784043e+00 -6.657201481785328e+00 1.28431e-12 4.64961e-12 2 -4.628506133793783e-01 -4.628506133744745e-01 4.90374e-12 1.65963e-11 3 -8.798307285704934e-01 -8.798307285918862e-01 2.13928e-11 7.57833e-11 ----------------------------------------------------------------------------------------------------- 9 C 1 3.519866402010301e-01 3.519866401998707e-01 1.15935e-12 2.84225e-11 2 -6.754648774665842e+00 -6.754648774669299e+00 3.45679e-12 1.71632e-11 3 2.490000495844879e+00 2.490000495841340e+00 3.53850e-12 3.26885e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 -2.890202619338716e+00 -2.890202619339745e+00 1.02851e-12 2.50959e-11 2 2.551965611417455e+00 2.551965611421896e+00 4.44089e-12 3.70166e-11 3 -4.622966404853444e+00 -4.622966404823519e+00 2.99254e-11 5.96847e-11 ----------------------------------------------------------------------------------------------------- 11 C 1 -1.242962319874881e+01 -1.242962319871835e+01 3.04663e-11 7.67546e-11 2 -1.296864749010368e+01 -1.296864749009315e+01 1.05356e-11 6.94200e-12 3 3.703958729016441e+00 3.703958729012214e+00 4.22684e-12 8.14802e-11 ----------------------------------------------------------------------------------------------------- 12 C 1 -3.818657699399000e+00 -3.818657699392797e+00 6.20259e-12 6.11591e-11 2 -3.974604956428910e-01 -3.974604956433013e-01 4.10227e-13 5.22498e-11 3 9.658336246398260e+00 9.658336246393500e+00 4.76064e-12 3.33849e-11 ----------------------------------------------------------------------------------------------------- 13 C 1 -5.573729918488475e+00 -5.573729918481539e+00 6.93579e-12 1.04927e-10 2 -5.469364949653678e+00 -5.469364949642067e+00 1.16112e-11 7.85736e-11 3 -1.585496015983063e+01 -1.585496015981921e+01 1.14184e-11 9.12515e-12 ----------------------------------------------------------------------------------------------------- 14 C 1 6.024221668648705e+00 6.024221668647375e+00 1.33049e-12 1.06260e-10 2 2.578623700892554e+00 2.578623700894723e+00 2.16849e-12 5.43445e-11 3 -5.239847252652406e+00 -5.239847252650153e+00 2.25242e-12 1.28135e-10 ----------------------------------------------------------------------------------------------------- 15 C 1 1.259768417561579e+01 1.259768417561278e+01 3.01270e-12 1.30852e-10 2 4.244912096022018e+00 4.244912096024868e+00 2.85016e-12 9.37801e-11 3 1.465214208315960e+01 1.465214208316932e+01 9.72555e-12 2.41819e-10 ----------------------------------------------------------------------------------------------------- 16 C 1 -2.122556957115632e+00 -2.122556957121536e+00 5.90372e-12 3.09071e-10 2 1.062407767486699e+01 1.062407767486367e+01 3.32001e-12 1.24398e-11 3 9.171121032033085e+00 9.171121032037547e+00 4.46221e-12 4.40785e-11 ----------------------------------------------------------------------------------------------------- 17 C 1 -3.419617519655033e+00 -3.419617519647931e+00 7.10187e-12 9.05764e-12 2 1.078477411626294e-02 1.078477412178449e-02 5.52155e-12 4.24440e-11 3 6.947939039189435e-01 6.947939039205101e-01 1.56664e-12 1.02480e-11 ----------------------------------------------------------------------------------------------------- 18 C 1 6.917373206037136e+00 6.917373205994236e+00 4.28999e-11 2.45556e-05 * 2 1.296933175126596e+00 1.296933175120169e+00 6.42641e-12 4.90573e-05 * 3 -6.168280110938961e+00 -6.168280110946630e+00 7.66853e-12 2.34849e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 5.342355569859484e+00 5.342355569860733e+00 1.24878e-12 1.12270e-10 2 7.624468861004870e+00 7.624468860979770e+00 2.50999e-11 1.30984e-10 3 3.420154238323093e+00 3.420154238306724e+00 1.63691e-11 3.60050e-11 ----------------------------------------------------------------------------------------------------- 20 C 1 1.104920359530252e+00 1.104920359530931e+00 6.79234e-13 6.87446e-11 2 -2.899156250404664e+00 -2.899156250420047e+00 1.53833e-11 3.08265e-11 3 -8.467369706983292e-01 -8.467369706958341e-01 2.49512e-12 1.21019e-10 ----------------------------------------------------------------------------------------------------- 21 C 1 -7.283458819176524e+00 -7.283458819165245e+00 1.12790e-11 9.42189e-11 2 2.668349613662975e+00 2.668349613659540e+00 3.43503e-12 9.42482e-11 3 1.448715530181485e+01 1.448715530184706e+01 3.22107e-11 2.42693e-10 ----------------------------------------------------------------------------------------------------- 22 C 1 6.314831380381822e+00 6.314831380373073e+00 8.74856e-12 3.59677e-11 2 4.866604478941208e+00 4.866604478909339e+00 3.18687e-11 2.43660e-05 * 3 1.230609137108390e+01 1.230609137114866e+01 6.47571e-11 3.12507e-10 ----------------------------------------------------------------------------------------------------- 23 C 1 -4.213925370262150e+00 -4.213925370264345e+00 2.19469e-12 1.37098e-10 2 4.155167639847884e+00 4.155167639844104e+00 3.77920e-12 3.35962e-11 3 -7.038868952847769e+00 -7.038868952843604e+00 4.16556e-12 5.20872e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 6.575365567717566e-01 6.575365567652466e-01 6.51001e-12 5.37516e-11 2 -9.324186768014213e+00 -9.324186768013108e+00 1.10489e-12 6.23963e-11 3 -8.153179849835148e+00 -8.153179849814499e+00 2.06484e-11 1.01041e-10 ----------------------------------------------------------------------------------------------------- 25 C 1 6.212225712761974e+00 6.212225712747497e+00 1.44773e-11 6.88924e-11 2 7.997256118449559e+00 7.997256118449856e+00 2.97540e-13 6.30216e-11 3 -1.102716311359172e+01 -1.102716311359719e+01 5.47296e-12 3.12887e-11 ----------------------------------------------------------------------------------------------------- 26 C 1 -2.560849744226354e+00 -2.560849744228671e+00 2.31681e-12 6.75917e-11 2 3.521931943309490e+00 3.521931943315043e+00 5.55289e-12 4.80145e-11 3 -4.702799863336478e+00 -4.702799863339262e+00 2.78355e-12 1.83682e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 -4.180406926405267e-01 -4.180406926627143e-01 2.21876e-11 2.47723e-10 2 -9.544463535129283e+00 -9.544463535129102e+00 1.81188e-13 1.60796e-11 3 4.214825882767851e+00 4.214825882761629e+00 6.22169e-12 5.56204e-11 ----------------------------------------------------------------------------------------------------- 28 C 1 -8.956930443390826e+00 -8.956930443387886e+00 2.93987e-12 6.49258e-11 2 1.419359019555614e+00 1.419359019559574e+00 3.95950e-12 1.28348e-11 3 -2.663559806152530e+00 -2.663559806150604e+00 1.92601e-12 8.90279e-10 * ----------------------------------------------------------------------------------------------------- 29 C 1 1.125034030101328e+00 1.125034030066540e+00 3.47871e-11 1.42191e-10 2 -4.679219887120844e+00 -4.679219887140005e+00 1.91607e-11 3.92662e-09 * 3 3.014613898544719e+00 3.014613898546798e+00 2.07923e-12 6.72533e-11 ----------------------------------------------------------------------------------------------------- 30 C 1 2.273192710817530e+00 2.273192710826692e+00 9.16156e-12 4.56200e-11 2 -3.219784725582279e+00 -3.219784725580353e+00 1.92601e-12 1.86708e-11 3 -4.990815121719090e+00 -4.990815121710808e+00 8.28226e-12 7.93881e-11 ----------------------------------------------------------------------------------------------------- 31 C 1 -2.461360352623131e+00 -2.461360352634498e+00 1.13669e-11 2.99032e-11 2 -2.117448280809827e+00 -2.117448280807882e+00 1.94511e-12 4.09597e-11 3 1.656101627728799e-01 1.656101627623970e-01 1.04828e-11 5.56085e-11 ----------------------------------------------------------------------------------------------------- 32 C 1 6.981708149197392e+00 6.981708149194862e+00 2.53042e-12 2.67715e-11 2 3.678685644273930e+00 3.678685644272782e+00 1.14841e-12 1.38676e-11 3 4.745613175919071e+00 4.745613175911238e+00 7.83285e-12 3.41069e-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 = 2: |F_model - F_numer| error = ----------------------- = 5.11977e-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. 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 -2.722780452674177e-01 -2.722780452565776e-01 1.08402e-11 7.59043e-12 2 -2.936805253441020e+00 -2.936805253440764e+00 2.56239e-13 5.96323e-12 3 -2.806932201368188e+00 -2.806932201365787e+00 2.40119e-12 1.06657e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 1.520255078515664e+00 1.520255078514630e+00 1.03428e-12 3.23366e-11 2 1.142756661742672e+00 1.142756661736330e+00 6.34248e-12 4.69450e-10 3 -4.202088644487734e+00 -4.202088644484586e+00 3.14859e-12 9.07532e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 2.732236636796640e+00 2.732236636800823e+00 4.18288e-12 7.08935e-11 2 -4.047522782762545e+00 -4.047522782755151e+00 7.39409e-12 4.09655e-11 3 -8.646128600102502e-01 -8.646128600037487e-01 6.50147e-12 1.86996e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -2.889720213882141e+00 -2.889720213893335e+00 1.11937e-11 6.55658e-11 2 5.400116749248142e+00 5.400116749253910e+00 5.76783e-12 2.25502e-10 3 1.842536710775337e+00 1.842536710737384e+00 3.79536e-11 1.45593e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 -9.899099286818243e-01 -9.899099286843189e-01 2.49467e-12 8.18345e-12 2 3.710259969224365e+00 3.710259969216800e+00 7.56417e-12 1.23875e-10 3 3.968265450678284e+00 3.968265450677400e+00 8.83738e-13 1.84781e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.445992214036164e+00 -2.445992214050285e+00 1.41211e-11 2.55413e-10 2 9.166857410329368e-01 9.166857410309163e-01 2.02049e-12 8.74333e-11 3 -3.386499327619118e-01 -3.386499327616276e-01 2.84162e-13 5.75788e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -2.887779733682464e+00 -2.887779733677994e+00 4.47020e-12 1.03667e-10 2 -3.494278117827389e-01 -3.494278117745539e-01 8.18501e-12 8.36855e-11 3 3.029252627795052e+00 3.029252627794999e+00 5.28466e-14 1.81530e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 -8.318955659841480e-01 -8.318955659810954e-01 3.05267e-12 3.11857e-10 2 7.924983343464483e-02 7.924983354126054e-02 1.06616e-10 1.33018e-10 3 1.805610547408516e+00 1.805610547399566e+00 8.94973e-12 4.65742e-10 ----------------------------------------------------------------------------------------------------- 9 Si 1 4.434677453571997e+00 4.434677453586153e+00 1.41567e-11 3.93108e-11 2 2.227543403862913e+00 2.227543403859555e+00 3.35820e-12 4.43645e-12 3 5.528483077464737e+00 5.528483077449021e+00 1.57163e-11 5.73976e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 -9.502209717658138e+00 -9.502209717670597e+00 1.24594e-11 3.77796e-11 2 -2.186768215302179e-01 -2.186768215156713e-01 1.45466e-11 4.51048e-11 3 -1.203809373001767e+00 -1.203809373002039e+00 2.71339e-13 5.29032e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 -1.470257827966793e+00 -1.470257827972679e+00 5.88551e-12 3.08324e-11 2 6.729463117257545e-01 6.729463117340909e-01 8.33644e-12 1.35324e-10 3 4.228859776662083e+00 4.228859776658251e+00 3.83249e-12 1.40147e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 5.076678421464221e+00 5.076678421465357e+00 1.13598e-12 2.56613e-11 2 -6.024452512126759e+00 -6.024452512120306e+00 6.45262e-12 8.50600e-11 3 4.632847920546004e-01 4.632847920456355e-01 8.96488e-12 4.29125e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 3.807115374025430e+00 3.807115374027498e+00 2.06812e-12 8.49676e-12 2 -1.056443469639304e+01 -1.056443469640719e+01 1.41505e-11 3.44899e-10 3 -5.714989446180729e+00 -5.714989446186514e+00 5.78471e-12 2.18439e-10 ----------------------------------------------------------------------------------------------------- 14 Si 1 1.627969294826239e+00 1.627969294832359e+00 6.11933e-12 4.65117e-12 2 -3.299489116436830e-01 -3.299489116448125e-01 1.12949e-12 3.31792e-11 3 7.416225856612788e-01 7.416225856486599e-01 1.26189e-11 7.87047e-11 ----------------------------------------------------------------------------------------------------- 15 Si 1 5.772526438609509e-01 5.772526438924090e-01 3.14582e-11 1.07118e-10 2 4.212312470022736e+00 4.212312470025293e+00 2.55707e-12 3.68843e-11 3 8.005385122252975e-01 8.005385122203856e-01 4.91185e-12 9.77067e-11 ----------------------------------------------------------------------------------------------------- 16 Si 1 3.038237042850399e+00 3.038237042847522e+00 2.87637e-12 5.27294e-11 2 5.738988060597803e+00 5.738988060616452e+00 1.86491e-11 1.30767e-10 3 8.988024777806283e+00 8.988024777826920e+00 2.06377e-11 1.07342e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -2.980591788278584e-01 -2.980591788264039e-01 1.45450e-12 4.10683e-11 2 2.421574948515484e+00 2.421574948521706e+00 6.22213e-12 4.58704e-11 3 2.540222188580727e+00 2.540222188578836e+00 1.89138e-12 8.54734e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 5.106972038987649e+00 5.106972038986741e+00 9.08607e-13 1.71381e-10 2 -1.647585179484754e+00 -1.647585179501049e+00 1.62945e-11 5.95883e-11 3 5.910208666413750e+00 5.910208666395857e+00 1.78932e-11 1.82506e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 7.407886766728640e+00 7.407886766747912e+00 1.92717e-11 2.58846e-10 2 4.809292546738229e+00 4.809292546753252e+00 1.50226e-11 9.62741e-11 3 -5.812734822070063e+00 -5.812734822078685e+00 8.62244e-12 2.89853e-10 ----------------------------------------------------------------------------------------------------- 20 Si 1 1.108856140503432e+00 1.108856140512643e+00 9.21085e-12 5.41738e-11 2 -3.053247650351892e+00 -3.053247650350459e+00 1.43263e-12 1.76126e-11 3 -3.553142059632534e+00 -3.553142059621993e+00 1.05409e-11 1.40076e-10 ----------------------------------------------------------------------------------------------------- 21 Si 1 -3.758371010812557e+00 -3.758371010866167e+00 5.36109e-11 2.04739e-10 2 2.143542002248715e+00 2.143542002060626e+00 1.88090e-10 4.13441e-10 3 3.578057199496866e-01 3.578057199526283e-01 2.94170e-12 1.51042e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 -7.733176795366810e-01 -7.733176795806080e-01 4.39271e-11 4.44566e-10 2 1.465115663853337e+00 1.465115663885213e+00 3.18756e-11 2.22078e-10 3 -2.047933690424866e+00 -2.047933690439602e+00 1.47362e-11 2.22330e-10 ----------------------------------------------------------------------------------------------------- 23 Si 1 -1.133393481923941e-01 -1.133393481801507e-01 1.22434e-11 9.59397e-11 2 3.854018013529258e-01 3.854018013529635e-01 3.77476e-14 3.03548e-11 3 8.178939817616353e-01 8.178939817531833e-01 8.45202e-12 3.46166e-11 ----------------------------------------------------------------------------------------------------- 24 Si 1 -4.360432536235045e+00 -4.360432536237340e+00 2.29505e-12 5.22613e-11 2 9.093463851028819e-01 9.093463851075699e-01 4.68803e-12 1.76796e-09 * 3 -3.609370044351204e+00 -3.609370044350575e+00 6.28830e-13 8.56097e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -3.055460147260805e+00 -3.055460147252284e+00 8.52163e-12 2.45830e-11 2 8.668704562371431e-01 8.668704562427832e-01 5.64016e-12 1.38454e-10 3 -4.480424157165623e+00 -4.480424157167858e+00 2.23466e-12 4.50245e-10 ----------------------------------------------------------------------------------------------------- 26 Si 1 3.330093274024939e+00 3.330093274017987e+00 6.95222e-12 1.06937e-10 2 1.666975869470889e+00 1.666975869456618e+00 1.42708e-11 9.49028e-11 3 -3.509637095260653e+00 -3.509637095262460e+00 1.80700e-12 1.13423e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 3.417838443064537e+00 3.417838443030768e+00 3.37690e-11 5.04337e-10 2 1.354518756923710e+00 1.354518756943865e+00 2.01557e-11 3.71871e-10 3 1.364414349597986e+00 1.364414349486869e+00 1.11116e-10 2.18851e-09 * ----------------------------------------------------------------------------------------------------- 28 Si 1 -2.456665873865132e+00 -2.456665873865701e+00 5.69322e-13 4.17506e-11 2 1.668237682375359e+00 1.668237682370915e+00 4.44444e-12 2.98960e-10 3 1.692609356278948e+00 1.692609356232931e+00 4.60172e-11 1.06304e-10 ----------------------------------------------------------------------------------------------------- 29 Si 1 -8.369627252972590e-01 -8.369627254760571e-01 1.78798e-10 5.87660e-09 * 2 -2.546339794306055e+00 -2.546339794296573e+00 9.48219e-12 1.05945e-10 3 -3.847576628087862e-01 -3.847576627762223e-01 3.25640e-11 1.73678e-09 * ----------------------------------------------------------------------------------------------------- 30 Si 1 -1.068326670201802e+00 -1.068326670198183e+00 3.61888e-12 1.04368e-10 2 -4.166599366161726e+00 -4.166599366185268e+00 2.35429e-11 1.85166e-10 3 -3.737832220799006e-01 -3.737832220810502e-01 1.14964e-12 1.50599e-10 ----------------------------------------------------------------------------------------------------- 31 Si 1 -2.219268823481058e+00 -2.219268823476675e+00 4.38272e-12 3.58233e-11 2 -3.176256052884321e+00 -3.176256052884211e+00 1.10134e-13 5.09224e-11 3 -3.238845352874838e+00 -3.238845352880732e+00 5.89395e-12 1.29812e-10 ----------------------------------------------------------------------------------------------------- 32 Si 1 -2.955821368351071e+00 -2.955821368357507e+00 6.43663e-12 9.96216e-11 2 -2.730438480841873e+00 -2.730438480852939e+00 1.10654e-11 2.32546e-10 3 -1.937922556635156e+00 -1.937922556650197e+00 1.50409e-11 4.72324e-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 = 8, direction = 2: |F_model - F_numer| error = ----------------------- = 1.34531e-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. MIXED STRUCTURE -- Species = C Si | a0 = 3.2955965838405064 | (Configuration in file "config-CSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -5.288786527037202e+00 -5.288786527067401e+00 3.01990e-11 3.46017e-11 2 -5.285155195908453e+00 -5.285155195906722e+00 1.73017e-12 1.10187e-11 3 -2.590096431834426e+00 -2.590096431830040e+00 4.38538e-12 1.14877e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 3.302678569536866e+00 3.302678569520743e+00 1.61231e-11 6.84783e-10 2 1.043298099086520e+01 1.043298099084842e+01 1.67830e-11 1.78748e-10 3 -7.569098026561634e+00 -7.569098026563486e+00 1.85185e-12 5.65716e-11 ----------------------------------------------------------------------------------------------------- 3 Si 1 5.895458667627205e+00 5.895458667616554e+00 1.06510e-11 2.83080e-10 2 -1.037660578476009e+01 -1.037660578475358e+01 6.51035e-12 9.83906e-11 3 -4.414680120157992e+00 -4.414680120163180e+00 5.18785e-12 5.27960e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -1.300800925571114e+01 -1.300800925570642e+01 4.72333e-12 5.13751e-10 2 3.365898057614997e-01 3.365898057696032e-01 8.10352e-12 1.73582e-10 3 -9.006439166035216e+00 -9.006439166055086e+00 1.98703e-11 9.98686e-11 ----------------------------------------------------------------------------------------------------- 5 C 1 -5.297009818544452e-03 -5.297009821243280e-03 2.69883e-12 7.67451e-11 2 1.854361988274062e+00 1.854361988275271e+00 1.20948e-12 1.42766e-11 3 9.717674744812781e-01 9.717674744784638e-01 2.81430e-12 1.10421e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 8.225770608413120e+00 8.225770608444204e+00 3.10845e-11 2.53401e-10 2 -1.771656162617984e+01 -1.771656162618212e+01 2.28084e-12 5.91882e-11 3 -7.457401193044771e+00 -7.457401193041852e+00 2.91944e-12 1.03780e-10 ----------------------------------------------------------------------------------------------------- 7 C 1 -3.235656841708627e-01 -3.235656841724665e-01 1.60383e-12 2.16876e-10 2 4.776810495749787e+00 4.776810495748809e+00 9.77884e-13 1.61275e-11 3 3.824952478680102e+00 3.824952478680868e+00 7.65166e-13 1.22040e-11 ----------------------------------------------------------------------------------------------------- 8 Si 1 2.341035451671455e+00 2.341035451721485e+00 5.00298e-11 4.91503e-10 2 -6.551826420854282e-01 -6.551826420903605e-01 4.93228e-12 1.66274e-10 3 -3.043594411576964e+00 -3.043594411590649e+00 1.36855e-11 7.16431e-11 ----------------------------------------------------------------------------------------------------- 9 C 1 2.066078114634611e+00 2.066078114630678e+00 3.93285e-12 1.93752e-11 2 -2.930314181066072e+00 -2.930314181056410e+00 9.66116e-12 3.29625e-11 3 7.391139479065639e-03 7.391139478028132e-03 1.03751e-12 4.10302e-11 ----------------------------------------------------------------------------------------------------- 10 C 1 2.698926505691831e+00 2.698926505693036e+00 1.20481e-12 6.19078e-11 2 -2.845609164724461e+00 -2.845609164723748e+00 7.13651e-13 1.45910e-11 3 1.705491512458771e-01 1.705491512458160e-01 6.11455e-14 7.24706e-12 ----------------------------------------------------------------------------------------------------- 11 C 1 8.980106378225085e-03 8.980106354277741e-03 2.39473e-11 2.66247e-09 * 2 2.858198283048521e+00 2.858198283042911e+00 5.61018e-12 2.59388e-11 3 -2.310998898954236e+00 -2.310998898937992e+00 1.62443e-11 1.51772e-10 ----------------------------------------------------------------------------------------------------- 12 Si 1 1.795739847184710e+00 1.795739847188860e+00 4.15001e-12 9.93221e-11 2 1.603074657018921e+00 1.603074657019269e+00 3.47722e-13 1.28246e-10 3 1.164295517999205e+00 1.164295518000071e+00 8.66196e-13 8.34128e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 -1.387809502956357e+01 -1.387809502949231e+01 7.12621e-11 5.13648e-10 2 1.879305940829678e+01 1.879305940827608e+01 2.07052e-11 4.38327e-10 3 -2.026743789400447e+00 -2.026743789406738e+00 6.29141e-12 9.32165e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 1.960473610228163e+00 1.960473610230726e+00 2.56350e-12 3.55864e-11 2 1.295120492001684e+00 1.295120491996635e+00 5.04907e-12 2.87019e-11 3 6.428633040581689e-01 6.428633040543860e-01 3.78297e-12 2.46906e-11 ----------------------------------------------------------------------------------------------------- 15 C 1 3.781012054270772e+00 3.781012054253317e+00 1.74558e-11 3.24594e-10 2 8.016882181956928e+00 8.016882181931736e+00 2.51923e-11 1.28927e-05 * 3 7.892364504668324e+00 7.892364504669063e+00 7.38964e-13 7.25802e-11 ----------------------------------------------------------------------------------------------------- 16 C 1 2.777076033645500e+00 2.777076033639431e+00 6.06892e-12 1.03121e-10 2 -3.969832739060623e+00 -3.969832739062364e+00 1.74127e-12 4.35962e-12 3 1.048014343730158e+01 1.048014343727513e+01 2.64517e-11 1.67596e-10 ----------------------------------------------------------------------------------------------------- 17 Si 1 -3.317322243613853e+00 -3.317322243611461e+00 2.39231e-12 5.15024e-11 2 -1.346682195079138e+01 -1.346682195074488e+01 4.65032e-11 1.71420e-09 * 3 1.638938304862142e+01 1.638938304843828e+01 1.83139e-10 1.61140e-09 * ----------------------------------------------------------------------------------------------------- 18 Si 1 1.428180588871176e+01 1.428180588870656e+01 5.19762e-12 2.50267e-10 2 7.296022471923325e+00 7.296022471878373e+00 4.49516e-11 3.12321e-10 3 1.841341557817307e+01 1.841341557816935e+01 3.71969e-12 1.62512e-10 ----------------------------------------------------------------------------------------------------- 19 C 1 -2.453457279318383e-01 -2.453457279265486e-01 5.28977e-12 9.55475e-11 2 -2.124651750068387e+00 -2.124651750089952e+00 2.15654e-11 5.75593e-11 3 -1.089682089143078e+01 -1.089682089143453e+01 3.74634e-12 1.45770e-10 ----------------------------------------------------------------------------------------------------- 20 C 1 -2.719796105743380e-01 -2.719796105324041e-01 4.19339e-11 8.73559e-11 2 1.111653336801195e+00 1.111653336605736e+00 1.95459e-10 5.90974e-10 3 -1.284076462713549e+00 -1.284076462737432e+00 2.38831e-11 9.93334e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 -1.394022692500999e+01 -1.394022692479601e+01 2.13985e-10 3.02563e-10 2 -8.018162540268492e+00 -8.018162540255826e+00 1.26654e-11 9.10063e-11 3 3.321086877791182e+00 3.321086877785753e+00 5.42899e-12 5.25933e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.102142960594671e+01 1.102142960600691e+01 6.02025e-11 1.93724e-10 2 3.320179046791596e+00 3.320179046878563e+00 8.69669e-11 1.05161e-09 * 3 -4.490236531955414e+00 -4.490236531599095e+00 3.56319e-10 1.58491e-09 * ----------------------------------------------------------------------------------------------------- 23 Si 1 3.193116862616140e+00 3.193116862638929e+00 2.27884e-11 4.68443e-11 2 1.184910735900573e-01 1.184910735890641e-01 9.93136e-13 3.10279e-11 3 1.041306919434304e+01 1.041306919434585e+01 2.81197e-12 3.23936e-11 ----------------------------------------------------------------------------------------------------- 24 C 1 -3.098221406640218e-01 -3.098221406651989e-01 1.17706e-12 4.28573e-11 2 -2.578336270767848e+00 -2.578336270769861e+00 2.01306e-12 2.00209e-11 3 -4.321455413369347e+00 -4.321455413367022e+00 2.32525e-12 4.30136e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -3.844900931993286e+00 -3.844900931982087e+00 1.11990e-11 1.96555e-10 2 1.503331091697423e+01 1.503331091700099e+01 2.67555e-11 3.28583e-10 3 9.747116543438526e+00 9.747116543429174e+00 9.35252e-12 2.26239e-10 ----------------------------------------------------------------------------------------------------- 26 C 1 -8.743711900978106e+00 -8.743711900960148e+00 1.79572e-11 6.34959e-11 2 -3.826987282874050e+00 -3.826987282870897e+00 3.15303e-12 4.86939e-11 3 5.739600457185543e+00 5.739600457169864e+00 1.56790e-11 3.73327e-10 ----------------------------------------------------------------------------------------------------- 27 C 1 1.240437476664602e+01 1.240437476668127e+01 3.52536e-11 1.54504e-10 2 9.756075049152903e+00 9.756075049131784e+00 2.11191e-11 1.56596e-04 * 3 -8.629184321607749e+00 -8.629184321591726e+00 1.60227e-11 2.09747e-10 ----------------------------------------------------------------------------------------------------- 28 C 1 4.929352425376319e+00 4.929352425373152e+00 3.16724e-12 2.03608e-10 2 -2.072715405387944e+00 -2.072715405385883e+00 2.06102e-12 2.57305e-11 3 -6.682231749943090e+00 -6.682231749945950e+00 2.85993e-12 9.32454e-11 ----------------------------------------------------------------------------------------------------- 29 C 1 -2.107946618606023e+00 -2.107946618578379e+00 2.76441e-11 5.72883e-06 * 2 4.353248104120634e+00 4.353248104147711e+00 2.70770e-11 1.94786e-11 3 -2.362239317248867e+00 -2.362239317246242e+00 2.62546e-12 1.58207e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 -8.677542739172146e+00 -8.677542739162197e+00 9.94937e-12 6.40874e-11 2 -7.412085309865835e+00 -7.412085309859245e+00 6.58940e-12 2.47651e-11 3 -8.893297997908679e+00 -8.893297997914381e+00 5.70211e-12 1.36160e-10 ----------------------------------------------------------------------------------------------------- 31 C 1 -1.326448268329993e+00 -1.326448268332852e+00 2.85949e-12 8.27940e-11 2 -4.406502625236124e-01 -4.406502625845258e-01 6.09134e-11 2.35219e-10 3 -6.285923832169162e-01 -6.285923831869102e-01 3.00060e-11 4.07508e-10 ----------------------------------------------------------------------------------------------------- 32 C 1 -5.394308505404458e+00 -5.394308505414771e+00 1.03126e-11 6.52927e-11 2 -7.236386195994823e+00 -7.236386195986427e+00 8.39684e-12 5.31228e-11 3 -2.570811600506331e+00 -2.570811600499082e+00 7.24842e-12 6.68505e-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 = 5, direction = 1: |F_model - F_numer| error = ----------------------- = 5.09500e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.34531e-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: A Comment: The letter grade A was assigned because the normalized error in the computation was 1.34531e-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.