!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_KimLee_2008_TiN__MO_070542625990_002 Supported species : N Ti 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 = N | a0 = 8.375 | (Configuration in file "config-N.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 -1.810839189408027e-02 -1.810839189405249e-02 2.77764e-14 9.42414e-11 * 2 -1.577487100685711e-02 -1.577487100666536e-02 1.91760e-13 1.61093e-11 3 -1.610483768966815e-02 -1.610483768905231e-02 6.15841e-13 8.01562e-11 * ----------------------------------------------------------------------------------------------------- 2 N 1 7.790943731128724e-02 7.790943731126325e-02 2.39947e-14 4.81531e-13 2 -1.661680048546952e-01 -1.661680048544775e-01 2.17687e-13 3.93094e-12 3 -1.476507667477953e-01 -1.476507667475334e-01 2.61846e-13 6.57588e-12 ----------------------------------------------------------------------------------------------------- 3 N 1 8.721875610021738e-02 8.721875609987940e-02 3.37980e-13 1.38901e-10 * 2 -1.126151242452254e-01 -1.126151242442265e-01 9.98895e-13 5.50976e-12 3 1.377592698166566e-02 1.377592698164328e-02 2.23814e-14 5.51015e-12 ----------------------------------------------------------------------------------------------------- 4 N 1 -1.866174522889490e-01 -1.866174522889903e-01 4.13558e-14 2.18545e-12 2 -6.721218684202224e-02 -6.721218684166047e-02 3.61766e-13 1.04618e-10 * 3 -5.457839824992265e-02 -5.457839825018472e-02 2.62075e-13 2.76894e-12 ----------------------------------------------------------------------------------------------------- 5 N 1 -2.155076576138285e-02 -2.155076576138579e-02 2.93515e-15 9.47638e-12 2 -1.402597409194703e-01 -1.402597409193042e-01 1.66089e-13 2.15083e-10 * 3 -1.399384550110436e-01 -1.399384550106269e-01 4.16694e-13 6.05049e-12 ----------------------------------------------------------------------------------------------------- 6 N 1 6.052200343077903e-02 6.052200343205367e-02 1.27464e-12 2.75919e-12 2 -9.803626595384091e-02 -9.803626595444898e-02 6.08069e-13 3.36352e-12 3 -1.559503877736989e-01 -1.559503877736221e-01 7.67442e-14 1.69129e-11 ----------------------------------------------------------------------------------------------------- 7 N 1 3.324334106166016e-02 3.324334106163274e-02 2.74156e-14 1.75495e-12 2 -3.539247813750599e-02 -3.539247813656304e-02 9.42954e-13 3.27684e-12 3 -1.051961959320176e-02 -1.051961959373572e-02 5.33960e-13 5.62722e-12 ----------------------------------------------------------------------------------------------------- 8 N 1 -3.968298428845920e-02 -3.968298428833696e-02 1.22242e-13 5.30997e-12 2 1.866153718527465e-01 1.866153718534797e-01 7.33219e-13 1.22627e-09 * 3 5.997020584318680e-02 5.997020584466514e-02 1.47833e-12 1.00778e-11 ----------------------------------------------------------------------------------------------------- 9 N 1 -9.035548937482887e-02 -9.035548937566289e-02 8.34013e-13 2.44028e-12 2 6.080167061248936e-02 6.080167061289051e-02 4.01151e-13 3.11837e-11 3 -3.078237380531412e-02 -3.078237380541791e-02 1.03799e-13 2.45709e-12 ----------------------------------------------------------------------------------------------------- 10 N 1 -7.059464590839361e-03 -7.059464591590642e-03 7.51282e-13 8.14427e-12 2 4.327704440260377e-02 4.327704440262987e-02 2.61041e-14 6.10709e-12 3 -3.881123625543620e-02 -3.881123625493403e-02 5.02168e-13 2.50092e-12 ----------------------------------------------------------------------------------------------------- 11 N 1 1.214006951619960e-02 1.214006951583241e-02 3.67187e-13 5.46502e-13 2 1.273027040145811e-01 1.273027040132692e-01 1.31190e-12 2.10608e-11 3 1.765589419132392e-02 1.765589419092865e-02 3.95278e-13 1.09364e-13 ----------------------------------------------------------------------------------------------------- 12 N 1 -2.334795132487501e-02 -2.334795132478312e-02 9.18952e-14 1.30409e-10 * 2 2.905106237155070e-02 2.905106236953840e-02 2.01230e-12 3.79155e-12 3 5.900036507369533e-03 5.900036504142009e-03 3.22752e-12 4.38400e-12 ----------------------------------------------------------------------------------------------------- 13 N 1 -1.638406187072370e-03 -1.638406186860894e-03 2.11476e-13 6.14623e-12 2 -1.528183634331984e-02 -1.528183634499145e-02 1.67161e-12 9.04480e-12 3 -6.659789847354425e-02 -6.659789847364890e-02 1.04652e-13 1.77116e-10 * ----------------------------------------------------------------------------------------------------- 14 N 1 8.223344927856295e-02 8.223344927891950e-02 3.56548e-13 4.03168e-12 2 2.271573730189796e-02 2.271573730170438e-02 1.93574e-13 1.93023e-12 3 -7.432846742565576e-02 -7.432846742631677e-02 6.61013e-13 5.02069e-12 ----------------------------------------------------------------------------------------------------- 15 N 1 4.913439700668326e-02 4.913439700633405e-02 3.49214e-13 9.16935e-12 2 1.898002768949951e-01 1.898002768953468e-01 3.51719e-13 2.91550e-12 3 -6.072285296066086e-03 -6.072285295942195e-03 1.23890e-13 6.14466e-12 ----------------------------------------------------------------------------------------------------- 16 N 1 -1.532276062089480e-01 -1.532276062059841e-01 2.96391e-12 2.19276e-11 2 5.559855942843993e-02 5.559855942988991e-02 1.44998e-12 9.35770e-12 3 -2.247458183365597e-02 -2.247458183314165e-02 5.14318e-13 3.49133e-12 ----------------------------------------------------------------------------------------------------- 17 N 1 -3.720938695401384e-02 -3.720938695301994e-02 9.93899e-13 4.32260e-12 2 -2.892711297350619e-02 -2.892711297316666e-02 3.39527e-13 2.16606e-12 3 -1.414980374906054e-03 -1.414980375247430e-03 3.41376e-13 3.59132e-12 ----------------------------------------------------------------------------------------------------- 18 N 1 7.869029920937719e-02 7.869029920921367e-02 1.63522e-13 1.81773e-08 * 2 -7.049166285495800e-02 -7.049166285497066e-02 1.26565e-14 3.62525e-12 3 -2.477892191838068e-04 -2.477892194101149e-04 2.26308e-13 8.85415e-12 ----------------------------------------------------------------------------------------------------- 19 N 1 -1.248380988975303e-02 -1.248380988926239e-02 4.90634e-13 1.28868e-11 2 -3.392461071453109e-02 -3.392461071479966e-02 2.68570e-13 4.37745e-11 3 4.390029168796322e-02 4.390029168857132e-02 6.08097e-13 9.50864e-12 ----------------------------------------------------------------------------------------------------- 20 N 1 -3.069375582372313e-02 -3.069375582506697e-02 1.34384e-12 3.08274e-11 2 7.378966485304176e-03 7.378966484933334e-03 3.70842e-13 7.68202e-12 3 2.385055075350674e-02 2.385055075351155e-02 4.81212e-15 4.71755e-13 ----------------------------------------------------------------------------------------------------- 21 N 1 1.041925054249177e-02 1.041925054287725e-02 3.85485e-13 1.66863e-12 2 -1.291271627127374e-01 -1.291271627122575e-01 4.79949e-13 4.08237e-12 3 6.312129826340376e-02 6.312129826465628e-02 1.25251e-12 3.52172e-12 ----------------------------------------------------------------------------------------------------- 22 N 1 4.041590607046001e-02 4.041590607065857e-02 1.98556e-13 7.56586e-12 2 -8.203813644444237e-02 -8.203813644505625e-02 6.13884e-13 1.38447e-11 3 1.138714003188980e-01 1.138714003188015e-01 9.64923e-14 2.65069e-12 ----------------------------------------------------------------------------------------------------- 23 N 1 3.065253869546304e-02 3.065253869529557e-02 1.67470e-13 6.69154e-11 * 2 -2.588690349750861e-02 -2.588690349771244e-02 2.03830e-13 2.51735e-12 3 1.678771713487402e-02 1.678771713466714e-02 2.06876e-13 1.49714e-12 ----------------------------------------------------------------------------------------------------- 24 N 1 -5.110924326862377e-02 -5.110924326876440e-02 1.40624e-13 1.48366e-08 * 2 -5.205673355219230e-03 -5.205673354904248e-03 3.14982e-13 9.15111e-11 * 3 2.558186581231233e-02 2.558186581244150e-02 1.29171e-13 3.09502e-08 * ----------------------------------------------------------------------------------------------------- 25 N 1 -1.105946129097335e-01 -1.105946129100964e-01 3.62863e-13 1.85970e-10 * 2 1.260178469256594e-01 1.260178469262218e-01 5.62328e-13 8.70434e-12 3 4.082212438740326e-02 4.082212438854013e-02 1.13688e-12 7.81521e-13 ----------------------------------------------------------------------------------------------------- 26 N 1 6.038192236454010e-04 6.038192246669235e-04 1.02152e-12 9.86942e-12 2 9.622785549711574e-02 9.622785549667959e-02 4.36151e-13 4.54102e-12 3 3.660620496471045e-02 3.660620496509862e-02 3.88162e-13 1.39177e-11 ----------------------------------------------------------------------------------------------------- 27 N 1 -2.445519907124851e-04 -2.445519911249733e-04 4.12488e-13 1.19695e-11 2 -9.415017403466302e-03 -9.415017403417977e-03 4.83242e-14 3.98506e-12 3 1.227563700219148e-02 1.227563700212541e-02 6.60652e-14 1.56752e-12 ----------------------------------------------------------------------------------------------------- 28 N 1 -2.816510562055205e-02 -2.816510562067541e-02 1.23360e-13 4.60821e-12 2 2.734923107093632e-02 2.734923107087258e-02 6.37441e-14 2.46352e-11 3 5.308263379071457e-02 5.308263378971452e-02 1.00005e-12 3.88825e-12 ----------------------------------------------------------------------------------------------------- 29 N 1 4.776657332084206e-02 4.776657332348976e-02 2.64770e-12 8.56192e-12 2 -3.007898770023370e-02 -3.007898770041465e-02 1.80952e-13 5.23612e-12 3 9.412211407945689e-02 9.412211407937257e-02 8.43214e-14 3.92486e-12 ----------------------------------------------------------------------------------------------------- 30 N 1 1.183019597001751e-01 1.183019597003707e-01 1.95677e-13 4.28742e-12 2 3.451597781798347e-02 3.451597781810819e-02 1.24720e-13 5.42161e-12 3 9.481552477180882e-02 9.481552477288706e-02 1.07823e-12 7.06027e-12 ----------------------------------------------------------------------------------------------------- 31 N 1 6.738583454950881e-02 6.738583454919179e-02 3.17010e-13 5.00083e-12 2 2.611932610497485e-02 2.611932610577294e-02 7.98084e-13 2.46404e-12 3 2.153773949662885e-02 2.153773949626568e-02 3.63164e-13 3.20329e-12 ----------------------------------------------------------------------------------------------------- 32 N 1 1.545134335919390e-02 1.545134335926250e-02 6.85979e-14 4.36512e-12 2 3.306414517826139e-02 3.306414517726364e-02 9.97744e-13 4.77633e-12 3 2.779491176167407e-02 2.779491176223026e-02 5.56184e-13 1.46539e-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 = 26, direction = 1: |F_model - F_numer| error = ----------------------- = 1.69177e-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 = Ti | a0 = 4.133002281188965 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 4.124627053823138e-01 4.124627053867599e-01 4.44611e-12 2.01601e-11 2 -2.065383610548076e-01 -2.065383610559469e-01 1.13931e-12 4.11668e-12 3 2.821055917980640e-01 2.821055918170779e-01 1.90139e-11 1.36872e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -9.964886405955108e-01 -9.964886405840252e-01 1.14856e-11 2.02993e-10 2 -3.193928579051643e-01 -3.193928579333670e-01 2.82028e-11 3.74970e-10 3 8.241209021696126e-01 8.241209021713597e-01 1.74705e-12 5.27744e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -3.489588543986687e-01 -3.489588543809130e-01 1.77557e-11 1.05240e-10 2 1.111388902766790e+00 1.111388902788831e+00 2.20408e-11 4.91736e-11 3 -7.279716544418890e-01 -7.279716544462623e-01 4.37328e-12 1.40116e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 7.136102766424642e-01 7.136102766389206e-01 3.54361e-12 1.83187e-10 2 -9.805614199264183e-01 -9.805614199364506e-01 1.00323e-11 6.49297e-11 3 -8.997328177251934e-03 -8.997328177599304e-03 3.47370e-13 1.19119e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -9.567274496352804e-01 -9.567274496456807e-01 1.04002e-11 1.27337e-10 2 -1.030113450605901e-01 -1.030113450510375e-01 9.55259e-12 1.71006e-09 * 3 -6.800367075584163e-02 -6.800367075032263e-02 5.51900e-12 1.46898e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -1.377242667052096e-01 -1.377242667027075e-01 2.50208e-12 4.99505e-10 2 3.171120402099096e-01 3.171120402095551e-01 3.54494e-13 1.47234e-10 3 2.008054405274256e-01 2.008054405434544e-01 1.60288e-11 8.69606e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 2.088263284331857e-01 2.088263284228822e-01 1.03035e-11 3.16361e-10 2 7.117527638696536e-02 7.117527635978101e-02 2.71844e-11 8.74982e-11 3 5.673078373008471e-01 5.673078373029896e-01 2.14251e-12 2.77223e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -4.260558214647545e-02 -4.260558213554509e-02 1.09304e-11 3.34156e-10 2 5.280624539347916e-01 5.280624538910689e-01 4.37227e-11 1.16110e-10 3 -2.341060511898887e+00 -2.341060511904671e+00 5.78426e-12 5.73318e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -1.891272464108098e-01 -1.891272463994599e-01 1.13499e-11 1.70989e-09 * 2 -3.315714176624280e-01 -3.315714176387506e-01 2.36773e-11 9.84089e-11 3 -2.376322817504595e-01 -2.376322817464056e-01 4.05390e-12 8.69419e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 1.166055444784279e+00 1.166055444786651e+00 2.37255e-12 9.22566e-11 2 3.229378897368338e-02 3.229378897005299e-02 3.63039e-12 3.82712e-11 3 2.229090561871349e-01 2.229090561898457e-01 2.71086e-12 3.00881e-09 * ----------------------------------------------------------------------------------------------------- 11 Ti 1 1.229639097716388e+00 1.229639097735808e+00 1.94202e-11 7.35194e-11 2 7.895906312439676e-01 7.895906312321810e-01 1.17866e-11 2.84431e-09 * 3 -4.387785076800950e-01 -4.387785076719824e-01 8.11262e-12 5.49365e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -2.650487312985458e-01 -2.650487313277907e-01 2.92448e-11 1.45462e-10 2 1.511652286888293e-01 1.511652286923393e-01 3.51000e-12 3.08788e-11 3 5.794639747898664e-01 5.794639747848750e-01 4.99145e-12 1.64260e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.905352268806193e-01 1.905352268837475e-01 3.12816e-12 1.19257e-10 2 6.618413988065049e-01 6.618413988540759e-01 4.75709e-11 8.92232e-11 3 -7.564862503223613e-02 -7.564862501373136e-02 1.85048e-11 1.76110e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -4.683842794774793e-01 -4.683842795045097e-01 2.70304e-11 1.05668e-09 2 -4.156790632663111e-01 -4.156790632588495e-01 7.46164e-12 7.77067e-11 3 3.949879296830611e-01 3.949879296731778e-01 9.88337e-12 1.12347e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 8.335197323997487e-01 8.335197324048075e-01 5.05873e-12 1.05805e-09 2 2.196593804879854e-03 2.196593776951964e-03 2.79279e-11 2.43842e-10 3 -9.600254991768105e-01 -9.600254991978496e-01 2.10392e-11 9.36526e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.009621187884393e+00 -1.009621187793683e+00 9.07101e-11 2.45633e-10 2 -1.708548456364067e-01 -1.708548456178631e-01 1.85436e-11 4.20216e-11 3 -4.204160369556367e-01 -4.204160369607344e-01 5.09764e-12 1.94044e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 8.322370317182816e-01 8.322370317183132e-01 3.16414e-14 1.39801e-10 2 2.580957960329994e-01 2.580957960386205e-01 5.62111e-12 8.13962e-11 3 -2.455636701459923e-01 -2.455636701377079e-01 8.28440e-12 1.35440e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -4.396336219198257e-01 -4.396336219948377e-01 7.50120e-11 3.36661e-10 2 -1.150051054151534e+00 -1.150051054197337e+00 4.58029e-11 3.24829e-11 3 -2.198489338313064e-01 -2.198489338074239e-01 2.38825e-11 1.84716e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -4.540492602575680e-01 -4.540492602618036e-01 4.23561e-12 8.80988e-11 2 -8.789591751536979e-02 -8.789591749984006e-02 1.55297e-11 3.53835e-09 * 3 -1.740986224867869e-02 -1.740986224846338e-02 2.15307e-13 1.13876e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 1.120132489256731e-02 1.120132485948526e-02 3.30821e-11 3.06340e-11 2 2.352419056147783e-01 2.352419056087076e-01 6.07073e-12 1.81295e-09 * 3 1.464853912732445e-01 1.464853912746842e-01 1.43963e-12 2.27605e-06 * ----------------------------------------------------------------------------------------------------- 21 Ti 1 -4.948225281442162e-01 -4.948225281632500e-01 1.90338e-11 4.14674e-10 2 -2.079678556490511e+00 -2.079678556495028e+00 4.51639e-12 1.49329e-10 3 1.258864199431033e+00 1.258864199438612e+00 7.57860e-12 2.96170e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.662436748475062e+00 1.662436748488465e+00 1.34028e-11 1.40888e-10 2 -1.281282248207867e+00 -1.281282248161780e+00 4.60860e-11 1.74041e-10 3 -1.132308994511546e+00 -1.132308994552054e+00 4.05080e-11 1.64406e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -6.368228284099084e-01 -6.368228283757237e-01 3.41848e-11 2.86115e-10 2 1.496168065228324e-01 1.496168065354389e-01 1.26065e-11 3.72797e-10 3 -3.697320575106411e-01 -3.697320574694914e-01 4.11496e-11 1.25775e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -3.111384727718562e-01 -3.111384728319455e-01 6.00893e-11 2.30590e-10 2 9.120957003908804e-01 9.120957004027113e-01 1.18309e-11 7.60223e-09 * 3 1.275882919624861e+00 1.275882919659421e+00 3.45601e-11 9.86550e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 5.520435652349601e-01 5.520435651944327e-01 4.05275e-11 2.04604e-09 * 2 7.386353143890481e-01 7.386353143559774e-01 3.30707e-11 2.68361e-10 3 9.160457788618647e-01 9.160457788783198e-01 1.64552e-11 1.56855e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -1.191114872161511e+00 -1.191114872169044e+00 7.53286e-12 1.88722e-09 * 2 -6.621442412351273e-01 -6.621442412036983e-01 3.14290e-11 6.33799e-10 3 -1.768503157358386e+00 -1.768503157365373e+00 6.98730e-12 9.25806e-11 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -4.591754067358773e-01 -4.591754067555382e-01 1.96609e-11 4.29509e-10 2 -8.522702189240272e-01 -8.522702189508763e-01 2.68491e-11 3.45836e-10 3 -6.445298675925579e-01 -6.445298675960348e-01 3.47689e-12 8.34462e-11 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -4.663068358666217e-01 -4.663068358946414e-01 2.80197e-11 1.91589e-09 * 2 -3.148662808533592e-01 -3.148662808687465e-01 1.53873e-11 2.39678e-11 3 -6.595297529285743e-02 -6.595297529420220e-02 1.34477e-12 2.97097e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.046756272918028e+00 -1.046756272835867e+00 8.21603e-11 8.40223e-11 2 1.749886018821849e+00 1.749886018772689e+00 4.91598e-11 1.76629e-10 3 1.491475891978216e+00 1.491475891950362e+00 2.78537e-11 4.27574e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 1.765716245339683e-01 1.765716245169697e-01 1.69986e-11 4.92133e-10 2 2.910132235405151e-01 2.910132234606717e-01 7.98434e-11 1.27493e-10 3 4.516600138921166e-01 4.516600139007764e-01 8.65980e-12 1.00274e-09 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -3.487553938814292e-02 -3.487553936812982e-02 2.00131e-11 3.33420e-11 2 1.025102694278073e+00 1.025102694279613e+00 1.53988e-12 1.50455e-10 3 5.979694584305029e-01 5.979694584030195e-01 2.74833e-11 2.30202e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 1.960242770032091e+00 1.960242770025082e+00 7.00862e-12 2.53089e-10 2 -6.871594651737506e-02 -6.871594654163954e-02 2.42645e-11 1.38601e-11 3 5.322992484132223e-01 5.322992484399021e-01 2.66798e-11 4.09921e-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 = 15, direction = 2: |F_model - F_numer| error = ----------------------- = 1.27142e-08 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 = N Ti | a0 = 3.656717525388509 | (Configuration in file "config-NTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 3.154882191748935e+00 3.154882191836202e+00 8.72671e-11 5.40039e-10 2 1.394552657798306e+00 1.394552657809694e+00 1.13887e-11 1.49182e-10 3 1.774442057363422e+00 1.774442057439664e+00 7.62415e-11 2.16966e-10 ----------------------------------------------------------------------------------------------------- 2 N 1 -1.374326179093021e+00 -1.374326179075112e+00 1.79086e-11 1.84836e-09 * 2 -5.434472438850444e+00 -5.434472438813765e+00 3.66782e-11 1.23623e-10 3 -3.701076456424837e+00 -3.701076456446051e+00 2.12137e-11 2.19631e-10 ----------------------------------------------------------------------------------------------------- 3 N 1 9.088462714369615e-01 9.088462714290372e-01 7.92433e-12 2.81152e-10 2 2.186684371770618e+00 2.186684371658132e+00 1.12486e-10 7.31285e-10 3 -7.228320515159393e+00 -7.228320515046235e+00 1.13157e-10 1.03783e-09 ----------------------------------------------------------------------------------------------------- 4 Ti 1 3.478311627271331e+00 3.478311627268922e+00 2.40918e-12 6.29764e-10 2 -2.853642240598847e+00 -2.853642240693541e+00 9.46940e-11 2.49216e-10 3 4.379214052000980e+00 4.379214051940246e+00 6.07336e-11 1.09307e-09 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -1.333284689466872e+00 -1.333284689485182e+00 1.83107e-11 1.95942e-09 * 2 2.617885344762976e+00 2.617885344724627e+00 3.83489e-11 1.46427e-10 3 1.299360743810447e+00 1.299360743763487e+00 4.69602e-11 8.44924e-11 ----------------------------------------------------------------------------------------------------- 6 N 1 -6.479971894775541e-01 -6.479971895002702e-01 2.27161e-11 2.06362e-10 2 -2.560900614387037e+00 -2.560900614374338e+00 1.26983e-11 6.13362e-10 3 3.605189261341343e+00 3.605189261340033e+00 1.31006e-12 1.74885e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -2.522021587474272e+00 -2.522021587470615e+00 3.65663e-12 3.21540e-10 2 1.471833309950239e+00 1.471833309977727e+00 2.74876e-11 2.53491e-09 * 3 1.323466959941319e+00 1.323466959886700e+00 5.46192e-11 1.46736e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -5.510737130575088e+00 -5.510737130477271e+00 9.78178e-11 4.43515e-10 2 -2.789376603588000e+00 -2.789376603531079e+00 5.69207e-11 1.10752e-10 3 4.420163246614611e-01 4.420163245493733e-01 1.12088e-10 4.31269e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 1.887574394333821e+00 1.887574394368669e+00 3.48477e-11 8.58102e-11 2 -8.887222779955529e-01 -8.887222780049271e-01 9.37417e-12 3.77777e-11 3 -1.301508273107473e+00 -1.301508273103046e+00 4.42690e-12 3.25708e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -2.112456505403122e+00 -2.112456505403228e+00 1.06137e-13 3.10895e-10 2 -1.774718219905774e+00 -1.774718219857971e+00 4.78031e-11 2.27533e-10 3 -4.015325041405239e+00 -4.015325041502718e+00 9.74785e-11 2.30473e-10 ----------------------------------------------------------------------------------------------------- 11 N 1 -1.015299971148232e+00 -1.015299971131784e+00 1.64486e-11 1.82340e-10 2 1.191862676209975e+01 1.191862676216763e+01 6.78799e-11 7.65557e-11 3 -2.498093416767727e+00 -2.498093416848198e+00 8.04707e-11 2.39426e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 3.666177475552531e-01 3.666177474089349e-01 1.46318e-10 2.85949e-10 2 -2.004307637798877e+00 -2.004307637849233e+00 5.03562e-11 2.82245e-10 3 3.559070678215587e+00 3.559070678282692e+00 6.71050e-11 2.37229e-10 ----------------------------------------------------------------------------------------------------- 13 N 1 -3.424352205851568e+00 -3.424352205823006e+00 2.85616e-11 2.57459e-09 * 2 3.187787457050485e+00 3.187787457038179e+00 1.23057e-11 4.15736e-10 3 4.539550251070301e+00 4.539550251085402e+00 1.51008e-11 1.72102e-09 * ----------------------------------------------------------------------------------------------------- 14 N 1 6.094814211974556e-02 6.094814209390420e-02 2.58414e-11 9.23632e-11 2 4.514513744431966e-01 4.514513744407685e-01 2.42806e-12 3.93672e-11 3 3.636393545952308e+00 3.636393545934096e+00 1.82121e-11 1.98773e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 1.725628031396487e+00 1.725628031362763e+00 3.37246e-11 2.78612e-10 2 8.638392896459419e-02 8.638392897326612e-02 8.67192e-12 1.54662e-10 3 -2.059573008051637e+00 -2.059573008057799e+00 6.16174e-12 3.03210e-09 * ----------------------------------------------------------------------------------------------------- 16 Ti 1 3.797849598610160e+00 3.797849598596406e+00 1.37548e-11 3.83016e-10 2 -4.606018463554000e+00 -4.606018463556437e+00 2.43627e-12 2.54445e-09 * 3 1.834075161877265e+00 1.834075162076314e+00 1.99049e-10 9.24247e-10 ----------------------------------------------------------------------------------------------------- 17 N 1 -4.291089407473518e+00 -4.291089407498325e+00 2.48077e-11 2.56402e-10 2 1.251913248322577e+00 1.251913248352379e+00 2.98024e-11 6.03149e-11 3 4.471195718099449e+00 4.471195718118238e+00 1.87894e-11 2.45115e-09 * ----------------------------------------------------------------------------------------------------- 18 N 1 -1.199539688902441e+00 -1.199539688899585e+00 2.85572e-12 6.58300e-11 2 -3.297794543099393e-01 -3.297794542055830e-01 1.04356e-10 4.84750e-10 3 2.093498685559163e+00 2.093498685513319e+00 4.58433e-11 1.34925e-08 * ----------------------------------------------------------------------------------------------------- 19 Ti 1 -1.550345990470985e+00 -1.550345990504243e+00 3.32581e-11 3.64473e-10 2 4.443529022253655e+00 4.443529022229495e+00 2.41602e-11 8.67004e-11 3 -4.108632027668413e+00 -4.108632027728389e+00 5.99760e-11 1.63262e-10 ----------------------------------------------------------------------------------------------------- 20 N 1 3.134812747741788e+00 3.134812747749598e+00 7.81064e-12 1.60462e-10 2 -5.517175362563512e+00 -5.517175362538783e+00 2.47296e-11 5.93196e-09 * 3 6.117248049549857e+00 6.117248049545481e+00 4.37606e-12 2.36577e-10 ----------------------------------------------------------------------------------------------------- 21 N 1 -1.367479404824748e+00 -1.367479404811535e+00 1.32125e-11 3.93341e-10 2 -9.065896382749157e-01 -9.065896382990344e-01 2.41187e-11 2.81486e-10 3 -1.933937596131536e+00 -1.933937596098255e+00 3.32812e-11 7.45017e-11 ----------------------------------------------------------------------------------------------------- 22 N 1 1.048929449758159e+01 1.048929449772471e+01 1.43121e-10 3.86617e-10 2 5.239338507444177e+00 5.239338507689665e+00 2.45488e-10 4.31280e-10 3 -8.472206913132910e+00 -8.472206913098256e+00 3.46532e-11 3.39510e-10 ----------------------------------------------------------------------------------------------------- 23 N 1 1.558685201680786e+00 1.558685201679430e+00 1.35514e-12 4.93010e-10 2 -1.309904581046782e+00 -1.309904581045838e+00 9.44356e-13 1.06958e-10 3 2.590964676319250e+00 2.590964676333816e+00 1.45666e-11 1.13184e-10 ----------------------------------------------------------------------------------------------------- 24 N 1 -6.627627734140338e+00 -6.627627734174614e+00 3.42757e-11 7.99229e-09 * 2 3.071869229718928e+00 3.071869229683651e+00 3.52771e-11 1.24709e-09 3 9.190847517052449e+00 9.190847517037255e+00 1.51932e-11 2.54236e-10 ----------------------------------------------------------------------------------------------------- 25 N 1 4.974074802998852e+00 4.974074802949857e+00 4.89955e-11 2.13692e-10 2 3.115364054615040e+00 3.115364054518239e+00 9.68012e-11 3.08596e-10 3 -6.853326937299568e+00 -6.853326937246881e+00 5.26867e-11 1.63459e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 1.937126727401822e+00 1.937126727416523e+00 1.47007e-11 5.33426e-10 2 -7.766259949524719e-01 -7.766259949774121e-01 2.49403e-11 2.68296e-10 3 -2.180186503792017e+00 -2.180186503818204e+00 2.61871e-11 1.34291e-09 ----------------------------------------------------------------------------------------------------- 27 Ti 1 3.262692128922391e+00 3.262692128908768e+00 1.36233e-11 2.20282e-10 2 -7.201962680344145e+00 -7.201962680332408e+00 1.17364e-11 2.32581e-10 3 -1.706023384108522e+00 -1.706023384114917e+00 6.39488e-12 1.18446e-09 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -1.972995891445779e+00 -1.972995891444777e+00 1.00209e-12 2.94044e-10 2 5.135791162238367e-01 5.135791162217027e-01 2.13396e-12 3.89570e-10 3 -8.779766185629601e-02 -8.779766187225971e-02 1.59637e-11 1.37398e-10 ----------------------------------------------------------------------------------------------------- 29 N 1 1.064259531192557e+00 1.064259531209415e+00 1.68578e-11 5.36859e-11 2 -3.393810312349489e-01 -3.393810312866644e-01 5.17155e-11 4.75153e-10 3 -3.224871665270487e+00 -3.224871665280828e+00 1.03411e-11 1.07469e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -2.061174050449557e+00 -2.061174050500458e+00 5.09006e-11 8.93592e-11 2 -7.537459139070204e-01 -7.537459139121367e-01 5.11635e-12 1.02152e-10 3 2.399713715106492e+00 2.399713715141058e+00 3.45666e-11 3.38632e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -4.394618858199983e+00 -4.394618858146577e+00 5.34062e-11 5.83817e-11 2 -1.015028257365242e+00 -1.015028257399662e+00 3.44196e-11 1.98298e-09 * 3 -3.455103377827220e+00 -3.455103377831782e+00 4.56168e-12 2.28817e-10 ----------------------------------------------------------------------------------------------------- 32 N 1 -3.962571575954015e-01 -3.962571576168367e-01 2.14352e-11 5.02756e-11 2 1.115530252591290e-01 1.115530252664115e-01 7.28252e-12 1.65038e-10 3 -4.302646199178179e-01 -4.302646199166423e-01 1.17562e-12 4.22929e-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 = 14, direction = 1: |F_model - F_numer| error = ----------------------- = 4.23989e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.27142e-08 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 1.27142e-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.