!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_Buckingham_MatsuiAkaogi_1991_TiO__SM_690504433912_000 Supported species : O 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 = O | a0 = 3.561929702758789 | (Configuration in file "config-O.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 O 1 -1.275240421287907e+01 -1.275240421286342e+01 1.56426e-11 1.05551e-10 2 -1.291359118952272e+01 -1.291359118951345e+01 9.27258e-12 1.06652e-10 3 -1.311483820709683e+01 -1.311483820708031e+01 1.65272e-11 1.36149e-10 ----------------------------------------------------------------------------------------------------- 2 O 1 -4.618460454301378e+00 -4.618460454300382e+00 9.95648e-13 1.63791e-10 2 -3.780458571577094e+00 -3.780458571588491e+00 1.13975e-11 1.84926e-10 3 -1.921476708264207e+01 -1.921476708262394e+01 1.81295e-11 1.78559e-11 ----------------------------------------------------------------------------------------------------- 3 O 1 -4.682867134839392e+00 -4.682867134824959e+00 1.44329e-11 4.65983e-11 2 -1.922922986314837e+01 -1.922922986315046e+01 2.09255e-12 2.31910e-10 3 -4.057299150985140e+00 -4.057299150961426e+00 2.37144e-11 2.14167e-10 ----------------------------------------------------------------------------------------------------- 4 O 1 -1.921246894468855e+01 -1.921246894469951e+01 1.09637e-11 1.40915e-10 2 -3.341071153056383e+00 -3.341071153062605e+00 6.22125e-12 9.87961e-11 3 -2.497033539157608e+00 -2.497033539138223e+00 1.93845e-11 9.13403e-11 ----------------------------------------------------------------------------------------------------- 5 O 1 4.394964094859624e+00 4.394964094843584e+00 1.60405e-11 1.01888e-10 2 -1.828255064413401e+01 -1.828255064424040e+01 1.06397e-10 2.28088e-10 3 -1.447560190299859e+01 -1.447560190300567e+01 7.08056e-12 2.44214e-11 ----------------------------------------------------------------------------------------------------- 6 O 1 1.522395401987774e+01 1.522395401987615e+01 1.58451e-12 2.02464e-10 2 -4.351485947776348e+00 -4.351485947796590e+00 2.02416e-11 1.06244e-10 3 -1.630814296129443e+01 -1.630814296127859e+01 1.58309e-11 5.21183e-12 ----------------------------------------------------------------------------------------------------- 7 O 1 1.672025238949349e+01 1.672025238946805e+01 2.54374e-11 7.00027e-11 2 -2.224877180816179e+01 -2.224877180818567e+01 2.38813e-11 1.66246e-10 3 -8.876673205183574e+00 -8.876673205199330e+00 1.57563e-11 3.17653e-10 ----------------------------------------------------------------------------------------------------- 8 O 1 1.741002667678014e+00 1.741002667674833e+00 3.18101e-12 2.41396e-10 2 -8.656337014849996e+00 -8.656337014835081e+00 1.49143e-11 2.12012e-10 3 -5.440940874718552e+00 -5.440940874697703e+00 2.08491e-11 2.63292e-10 ----------------------------------------------------------------------------------------------------- 9 O 1 -1.480344520674941e+01 -1.480344520675010e+01 6.94556e-13 1.54975e-10 2 3.670491562577414e+00 3.670491562602699e+00 2.52847e-11 5.98965e-10 3 -1.829681874517765e+01 -1.829681874517813e+01 4.79616e-13 2.17700e-10 ----------------------------------------------------------------------------------------------------- 10 O 1 -9.368898255229611e+00 -9.368898255172727e+00 5.68843e-11 4.93035e-10 2 1.818295609716811e+01 1.818295609715597e+01 1.21396e-11 2.52772e-10 3 -2.201042370598693e+01 -2.201042370600673e+01 1.97957e-11 3.97581e-10 ----------------------------------------------------------------------------------------------------- 11 O 1 -7.454518619566024e+00 -7.454518619561577e+00 4.44711e-12 2.45128e-10 2 1.346840842903767e+00 1.346840842924074e+00 2.03064e-11 1.96332e-10 3 -5.109656769531476e+00 -5.109656769517168e+00 1.43077e-11 2.72096e-10 ----------------------------------------------------------------------------------------------------- 12 O 1 -1.695397177758705e+01 -1.695397177757694e+01 1.01146e-11 1.48848e-10 2 1.623308698369418e+01 1.623308698370096e+01 6.78568e-12 8.99938e-11 3 -4.422921877894979e+00 -4.422921877912869e+00 1.78897e-11 4.39996e-10 ----------------------------------------------------------------------------------------------------- 13 O 1 -1.330947239438420e+00 -1.330947239452817e+00 1.43967e-11 2.93851e-10 2 -1.569441079788896e+00 -1.569441079796227e+00 7.33102e-12 4.79185e-10 3 -3.232359688454501e+01 -3.232359688452196e+01 2.30500e-11 4.20194e-10 ----------------------------------------------------------------------------------------------------- 14 O 1 1.441684626058352e+01 1.441684626058887e+01 5.34861e-12 5.55477e-10 2 1.538624310399860e+01 1.538624310401781e+01 1.92077e-11 1.34111e-10 3 -1.378098039383083e+01 -1.378098039383537e+01 4.53504e-12 2.93833e-10 ----------------------------------------------------------------------------------------------------- 15 O 1 3.002356880230934e+01 3.002356880222967e+01 7.96732e-11 2.14676e-10 2 3.158443565593799e+00 3.158443565625309e+00 3.15103e-11 1.87126e-11 3 2.945173650165814e+00 2.945173650110247e+00 5.55662e-11 3.81743e-10 ----------------------------------------------------------------------------------------------------- 16 O 1 8.393490880425135e+00 8.393490880319499e+00 1.05636e-10 3.12207e-10 2 2.628914081679688e+01 2.628914081685777e+01 6.08935e-11 5.55488e-10 3 4.100896004875806e+00 4.100896004883384e+00 7.57794e-12 3.03867e-10 ----------------------------------------------------------------------------------------------------- 17 O 1 -2.122258564194309e+01 -2.122258564192005e+01 2.30429e-11 2.31669e-10 2 -1.682891805264874e+01 -1.682891805261522e+01 3.35234e-11 2.41819e-10 3 -3.854432612624907e+00 -3.854432612477051e+00 1.47856e-10 5.73727e-10 ----------------------------------------------------------------------------------------------------- 18 O 1 -4.987473196018684e+00 -4.987473196045965e+00 2.72804e-11 3.00803e-10 2 -3.417643622436139e+00 -3.417643622501441e+00 6.53024e-11 4.63054e-10 3 4.880855295180862e+00 4.880855295154520e+00 2.63425e-11 4.48979e-10 ----------------------------------------------------------------------------------------------------- 19 O 1 3.641631742595088e+00 3.641631742546092e+00 4.89959e-11 3.88162e-10 2 -1.893538954897678e+01 -1.893538954894032e+01 3.64544e-11 2.77019e-10 3 1.864886149663787e+01 1.864886149666736e+01 2.94840e-11 6.82405e-10 ----------------------------------------------------------------------------------------------------- 20 O 1 -1.647200781650454e+01 -1.647200781646656e+01 3.79821e-11 6.20666e-10 2 2.776783831047167e+00 2.776783831008816e+00 3.83511e-11 6.17469e-10 3 1.820410835870971e+01 1.820410835870084e+01 8.87823e-12 2.36646e-11 ----------------------------------------------------------------------------------------------------- 21 O 1 2.857506707801235e+00 2.857506707806658e+00 5.42277e-12 2.65098e-10 2 -1.936227153408002e+01 -1.936227153407923e+01 7.92255e-13 2.23537e-10 3 6.762727205148696e+00 6.762727205159640e+00 1.09441e-11 4.05047e-10 ----------------------------------------------------------------------------------------------------- 22 O 1 2.196023172177231e+01 2.196023172178505e+01 1.27400e-11 6.82249e-10 2 1.054122265377513e+00 1.054122265331338e+00 4.61748e-11 1.82650e-10 3 9.872544064782423e+00 9.872544064801172e+00 1.87494e-11 8.45846e-10 ----------------------------------------------------------------------------------------------------- 23 O 1 1.239209220224248e+01 1.239209220223578e+01 6.70219e-12 3.88381e-10 2 -1.061210191125751e+01 -1.061210191121993e+01 3.75771e-11 1.69052e-10 3 1.308575492973229e+01 1.308575492972131e+01 1.09797e-11 4.79274e-10 ----------------------------------------------------------------------------------------------------- 24 O 1 3.890731411053640e+00 3.890731411046827e+00 6.81322e-12 1.91740e-11 2 -3.922389043372529e+00 -3.922389043378621e+00 6.09202e-12 3.84033e-10 3 1.918163881902488e+01 1.918163881907277e+01 4.78906e-11 3.95787e-10 ----------------------------------------------------------------------------------------------------- 25 O 1 -2.053988856009031e+01 -2.053988856001876e+01 7.15552e-11 3.88713e-10 2 2.891349373296718e+00 2.891349373261554e+00 3.51639e-11 6.48193e-11 3 5.078084572746259e+00 5.078084572745256e+00 1.00275e-12 2.73007e-10 ----------------------------------------------------------------------------------------------------- 26 O 1 -4.662107969820784e+00 -4.662107969738354e+00 8.24301e-11 2.03523e-10 2 2.218086579581811e+01 2.218086579587275e+01 5.46407e-11 1.45995e-10 3 4.344159303548347e+00 4.344159303624040e+00 7.56932e-11 3.55750e-10 ----------------------------------------------------------------------------------------------------- 27 O 1 -1.361327691809486e+00 -1.361327691722402e+00 8.70841e-11 4.52197e-10 2 -3.324577799880623e+00 -3.324577799892423e+00 1.17999e-11 3.24361e-10 3 1.912207339150150e+01 1.912207339158116e+01 7.96661e-11 1.31191e-10 ----------------------------------------------------------------------------------------------------- 28 O 1 -1.796147987630780e+01 -1.796147987628595e+01 2.18492e-11 2.49347e-10 2 1.752218448454787e+01 1.752218448451022e+01 3.76552e-11 8.63487e-11 3 1.263445612158024e+01 1.263445612157036e+01 9.88543e-12 1.38291e-10 ----------------------------------------------------------------------------------------------------- 29 O 1 4.555449240965282e+00 4.555449240955631e+00 9.65095e-12 1.50536e-10 2 4.088038332506920e+00 4.088038332521063e+00 1.41434e-11 1.77645e-10 3 7.680840748371782e+00 7.680840748296002e+00 7.57803e-11 7.15135e-11 ----------------------------------------------------------------------------------------------------- 30 O 1 1.607443285049386e+01 1.607443285048563e+01 8.22453e-12 1.11864e-10 2 1.736978604106048e+01 1.736978604104034e+01 2.01368e-11 3.63066e-10 3 1.962631256431291e+00 1.962631256290355e+00 1.40936e-10 2.64632e-10 ----------------------------------------------------------------------------------------------------- 31 O 1 1.858962258684902e+01 1.858962258695360e+01 1.04581e-10 8.34355e-11 2 4.329036888507419e-01 4.329036888639725e-01 1.32306e-11 1.41775e-10 3 1.783177340847199e+01 1.783177340843619e+01 3.58007e-11 6.66320e-09 * ----------------------------------------------------------------------------------------------------- 32 O 1 3.509075018773815e+00 3.509075018761340e+00 1.24749e-11 9.66742e-11 2 1.819299199942968e+01 1.819299199940811e+01 2.15685e-11 4.95032e-10 3 1.744754928675880e+01 1.744754928673170e+01 2.71001e-11 1.51442e-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 = 30, direction = 3: |F_model - F_numer| error = ----------------------- = 7.18096e-11 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 = 2.163208244368434 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 -1.214221203770506e+02 -1.214221203771579e+02 1.07278e-10 1.00471e-09 2 -9.973492764397825e+01 -9.973492764414115e+01 1.62899e-10 1.73351e-09 3 -1.142096956028133e+02 -1.142096956030437e+02 2.30429e-10 8.45773e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -1.652845387019562e+02 -1.652845387018936e+02 6.25562e-11 3.07060e-09 2 5.012609399450051e+01 5.012609399499880e+01 4.98297e-10 6.72081e-10 3 -2.634644873141113e+02 -2.634644873138832e+02 2.28056e-10 8.55096e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.764720633655061e+02 -1.764720633653676e+02 1.38499e-10 4.21326e-09 2 -2.580768095348840e+02 -2.580768095346792e+02 2.04807e-10 3.66992e-09 3 2.225381543248797e+00 2.225381542846153e+00 4.02645e-10 1.91169e-09 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -2.036619575070846e+02 -2.036619575058840e+02 1.20053e-09 1.54498e-09 2 -4.539838257143484e+01 -4.539838257131678e+01 1.18057e-10 7.36428e-09 3 -5.773273233807261e+01 -5.773273233843955e+01 3.66946e-10 1.15218e-09 ----------------------------------------------------------------------------------------------------- 5 Ti 1 8.009510154847587e+01 8.009510154826948e+01 2.06384e-10 8.34796e-08 * 2 -3.374695107374461e+02 -3.374695107358495e+02 1.59656e-09 3.61996e-09 3 -3.775476426152990e+02 -3.775476426153515e+02 5.25233e-11 2.49014e-09 ----------------------------------------------------------------------------------------------------- 6 Ti 1 2.458475488160007e+02 2.458475488156223e+02 3.78407e-10 7.60366e-10 2 -1.004877701713693e+02 -1.004877701713666e+02 2.67164e-12 2.35926e-09 3 -2.246601463713152e+02 -2.246601463715470e+02 2.31779e-10 2.52334e-09 ----------------------------------------------------------------------------------------------------- 7 Ti 1 2.436936884980706e+02 2.436936884979363e+02 1.34349e-10 2.29454e-09 2 -2.047419521587689e+02 -2.047419521589258e+02 1.56831e-10 1.19599e-09 3 -3.382814167822279e+01 -3.382814167864163e+01 4.18837e-10 1.81071e-08 * ----------------------------------------------------------------------------------------------------- 8 Ti 1 8.904800082801425e+01 8.904800082835942e+01 3.45167e-10 4.04128e-10 2 9.531940952249916e+01 9.531940952235493e+01 1.44226e-10 2.35293e-09 3 1.217572257861240e+02 1.217572257863016e+02 1.77593e-10 1.21520e-09 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -1.889031519910450e+02 -1.889031519906653e+02 3.79657e-10 2.30463e-09 2 -2.508028746932781e+01 -2.508028746897799e+01 3.49825e-10 7.72552e-10 3 -2.133972666808059e+02 -2.133972666809252e+02 1.19257e-10 1.09598e-08 ----------------------------------------------------------------------------------------------------- 10 Ti 1 6.773515214529450e+00 6.773515213984088e+00 5.45362e-10 4.41196e-10 2 1.628347898011762e+02 1.628347898007104e+02 4.65718e-10 2.19870e-09 3 -1.618727525502404e+02 -1.618727525499661e+02 2.74298e-10 2.35221e-09 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -1.440620965260111e+01 -1.440620965240966e+01 1.91443e-10 4.36637e-10 2 6.342892150736875e+01 6.342892150779805e+01 4.29303e-10 1.56766e-09 3 -9.671636971074246e+01 -9.671636971071250e+01 2.99565e-11 1.55507e-09 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -1.680459555084994e+02 -1.680459555086130e+02 1.13516e-10 5.98078e-10 2 2.096488296551889e+02 2.096488296553721e+02 1.83263e-10 1.90312e-09 3 2.838675632605275e+01 2.838675632530776e+01 7.44983e-10 2.36724e-09 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -1.223409666299360e+02 -1.223409666302790e+02 3.42979e-10 1.49308e-08 * 2 1.427781443485781e+02 1.427781443483324e+02 2.45677e-10 2.44566e-08 * 3 -2.920581538267872e+02 -2.920581538265933e+02 1.93950e-10 5.61886e-09 ----------------------------------------------------------------------------------------------------- 14 Ti 1 1.231484643796090e+02 1.231484643800511e+02 4.42029e-10 1.26479e-09 2 1.448206206079810e+02 1.448206206079440e+02 3.70051e-11 8.85962e-10 3 -1.315551999516685e+02 -1.315551999510851e+02 5.83356e-10 1.26687e-09 ----------------------------------------------------------------------------------------------------- 15 Ti 1 2.936429857514725e+02 2.936429857504509e+02 1.02153e-09 1.13744e-09 2 7.409422090864651e+01 7.409422090945228e+01 8.05770e-10 6.80402e-10 3 1.345093701496600e+02 1.345093701490720e+02 5.88045e-10 1.09199e-09 ----------------------------------------------------------------------------------------------------- 16 Ti 1 1.785617754628498e+01 1.785617754606950e+01 2.15479e-10 1.16837e-09 2 1.987366885916775e+02 1.987366885909773e+02 7.00140e-10 2.48768e-08 * 3 -7.739439455589729e+01 -7.739439455563368e+01 2.63611e-10 2.54494e-09 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -1.689475007447135e+02 -1.689475007448822e+02 1.68683e-10 2.46266e-09 2 -1.579693115359441e+02 -1.579693115365575e+02 6.13483e-10 3.84318e-10 3 3.793294971358510e+01 3.793294971363446e+01 4.93614e-11 5.30856e-09 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -1.328108624788635e+02 -1.328108624790732e+02 2.09667e-10 7.11566e-10 2 -1.386633360874468e+02 -1.386633360850049e+02 2.44185e-09 4.20496e-09 3 6.071607031759965e+01 6.071607031754167e+01 5.79803e-11 1.48517e-09 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -7.460424474942515e+01 -7.460424474913192e+01 2.93227e-10 2.73336e-09 2 -1.979827874902914e+02 -1.979827874905172e+02 2.25725e-10 4.88330e-09 3 1.715957648801470e+02 1.715957648798770e+02 2.70006e-10 3.74550e-09 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.808334650999579e+02 -1.808334650999821e+02 2.42721e-11 4.52690e-09 2 -9.326181837999033e+01 -9.326181838057778e+01 5.87448e-10 1.97653e-09 3 1.758925501801192e+02 1.758925501803650e+02 2.45819e-10 5.47303e-09 ----------------------------------------------------------------------------------------------------- 21 Ti 1 7.689077419107889e+01 7.689077419061728e+01 4.61611e-10 5.88052e-09 2 -2.353412649761244e+02 -2.353412649765382e+02 4.13849e-10 6.55348e-10 3 8.103243115782857e+01 8.103243115748515e+01 3.43420e-10 2.49511e-09 ----------------------------------------------------------------------------------------------------- 22 Ti 1 2.133146550296940e+02 2.133146550297776e+02 8.36451e-11 2.12722e-09 2 -1.827886902290175e+01 -1.827886902263844e+01 2.63313e-10 7.06606e-10 3 -3.388091812073217e+01 -3.388091812011938e+01 6.12793e-10 2.10695e-08 * ----------------------------------------------------------------------------------------------------- 23 Ti 1 1.319043247213417e+02 1.319043247212434e+02 9.83675e-11 2.29696e-09 2 -1.479906618044191e+02 -1.479906618059596e+02 1.54057e-09 4.31061e-09 3 2.110925996346404e+02 2.110925996344639e+02 1.76527e-10 2.57143e-09 ----------------------------------------------------------------------------------------------------- 24 Ti 1 1.049344126876729e+02 1.049344126864941e+02 1.17873e-09 2.29490e-09 2 -7.078801844252115e+01 -7.078801844319800e+01 6.76849e-10 2.81500e-09 3 2.647461751927003e+02 2.647461751921942e+02 5.06077e-10 1.47531e-09 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -3.344986043155867e+02 -3.344986043153007e+02 2.85979e-10 2.32143e-09 2 -1.515943791812376e+02 -1.515943791806891e+02 5.48482e-10 2.78393e-09 3 -6.163008549260240e+01 -6.163008549300426e+01 4.01855e-10 8.64077e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 1.553020740755667e+02 1.553020740754997e+02 6.69047e-11 3.91933e-09 2 2.905037453571957e+02 2.905037453577071e+02 5.11477e-10 2.09337e-09 3 -1.271600294168910e+02 -1.271600294172895e+02 3.98558e-10 2.50657e-09 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -7.602583394344909e+01 -7.602583394337415e+01 7.49338e-11 3.30488e-10 2 6.704543777307700e+01 6.704543777314824e+01 7.12390e-11 3.29748e-08 * 3 3.377158979399998e+02 3.377158979395402e+02 4.59636e-10 4.36776e-08 * ----------------------------------------------------------------------------------------------------- 28 Ti 1 -2.165940897705143e+02 -2.165940897720144e+02 1.50007e-09 3.48129e-09 2 3.269918564704387e+02 3.269918564709333e+02 4.94595e-10 4.72653e-09 3 4.095384817058133e+02 4.095384817067904e+02 9.77138e-10 7.86827e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 1.868826713694327e+02 1.868826713695469e+02 1.14142e-10 1.02364e-09 2 1.197988586081426e+02 1.197988586073488e+02 7.93847e-10 8.89258e-10 3 -8.642681529564842e+01 -8.642681529528903e+01 3.59393e-10 6.81172e-09 ----------------------------------------------------------------------------------------------------- 30 Ti 1 1.826323542173975e+02 1.826323542178922e+02 4.94623e-10 8.49639e-10 2 1.602891463793301e+02 1.602891463792856e+02 4.45368e-11 3.48754e-09 3 -2.164515521053555e+00 -2.164515521081216e+00 2.76610e-11 1.69931e-09 ----------------------------------------------------------------------------------------------------- 31 Ti 1 1.841072160260866e+02 1.841072160265971e+02 5.10511e-10 4.15494e-09 2 1.647961806392290e+01 1.647961806374015e+01 1.82752e-10 6.62939e-09 3 1.330021540329635e+02 1.330021540333011e+02 3.37508e-10 4.55623e-09 ----------------------------------------------------------------------------------------------------- 32 Ti 1 8.777599935460920e+00 8.777599935138328e+00 3.22592e-10 5.10945e-09 2 1.599637056183620e+02 1.599637056184591e+02 9.70886e-11 7.72559e-10 3 1.855555384824205e+02 1.855555384821242e+02 2.96296e-10 8.52225e-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 = 3, direction = 3: |F_model - F_numer| error = ----------------------- = 1.80933e-10 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = O Ti | a0 = 3.254726421402228 | (Configuration in file "config-OTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 -2.020301385248160e+01 -2.020301385249485e+01 1.32552e-11 1.28701e-10 2 -1.517320456969863e+01 -1.517320456969359e+01 5.04485e-12 4.72156e-11 3 -6.212097879842381e+00 -6.212097879840577e+00 1.80389e-12 4.27569e-12 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -5.401336443213957e+00 -5.401336443216260e+00 2.30305e-12 8.33775e-10 * 2 -1.559310342867655e+01 -1.559310342867869e+01 2.13873e-12 3.92752e-11 3 -1.421417181934815e+01 -1.421417181933810e+01 1.00489e-11 1.24611e-11 ----------------------------------------------------------------------------------------------------- 3 Ti 1 1.261466963576385e+01 1.261466963577783e+01 1.39835e-11 5.09477e-11 2 -2.038850137378307e+01 -2.038850137375710e+01 2.59739e-11 3.87423e-11 3 1.125240448229086e+01 1.125240448229984e+01 8.98126e-12 1.34406e-10 ----------------------------------------------------------------------------------------------------- 4 O 1 9.423292747049501e+00 9.423292747049002e+00 4.99156e-13 4.80611e-11 2 -7.285344258461165e+00 -7.285344258455050e+00 6.11511e-12 1.37519e-10 3 -1.415625630298698e+01 -1.415625630301940e+01 3.24185e-11 6.89546e-11 ----------------------------------------------------------------------------------------------------- 5 O 1 -2.811397653116511e+01 -2.811397653118856e+01 2.34515e-11 1.53346e-10 2 1.545143267576729e+01 1.545143267577146e+01 4.16556e-12 2.67590e-11 3 -2.194197448787365e+01 -2.194197448789721e+01 2.35509e-11 1.60242e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 2.990561549892162e+01 2.990561549893112e+01 9.49996e-12 3.90337e-11 2 -1.712880707967570e+01 -1.712880707967065e+01 5.04485e-12 2.05123e-10 3 2.506611713718262e+00 2.506611713710900e+00 7.36167e-12 7.92055e-11 ----------------------------------------------------------------------------------------------------- 7 O 1 1.220821538086273e+01 1.220821538080527e+01 5.74563e-11 8.28599e-11 2 1.314703022321096e+01 1.314703022321331e+01 2.35190e-12 7.89449e-11 3 1.765663369891982e+01 1.765663369892874e+01 8.92442e-12 2.77030e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.754157567835382e+01 1.754157567835103e+01 2.79243e-12 6.80558e-11 2 -7.710640805359639e+00 -7.710640805362861e+00 3.22142e-12 3.90923e-11 3 3.292500605447631e+01 3.292500605446800e+01 8.30624e-12 6.79918e-11 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -2.915417391049539e+01 -2.915417391050717e+01 1.17808e-11 3.42091e-11 2 -1.161311903679999e+00 -1.161311903682082e+00 2.08300e-12 1.29794e-10 3 2.706901959463442e+00 2.706901959471067e+00 7.62501e-12 7.05649e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 1.001479083053481e+01 1.001479083055426e+01 1.94529e-11 2.44009e-10 2 2.922442349171116e+01 2.922442349173041e+01 1.92522e-11 3.23190e-11 3 2.793795776517300e+00 2.793795776517008e+00 2.91323e-13 3.58602e-11 ----------------------------------------------------------------------------------------------------- 11 O 1 -2.059868096108483e+01 -2.059868096108835e+01 3.51363e-12 1.59588e-11 2 1.839463505944128e+00 1.839463505925823e+00 1.83049e-11 8.89631e-11 3 -3.733450513338488e+01 -3.733450513338462e+01 2.62901e-13 3.41089e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -1.574894846570020e+01 -1.574894846570078e+01 5.86198e-13 1.15495e-10 2 1.405778943237017e+01 1.405778943236223e+01 7.93854e-12 1.25480e-10 3 2.339490215703074e+01 2.339490215701739e+01 1.33475e-11 3.99680e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 2.139398309238982e+01 2.139398309237527e+01 1.45519e-11 1.35699e-10 2 1.475993218204894e+01 1.475993218208320e+01 3.42570e-11 2.86882e-11 3 1.129347245545524e+00 1.129347245582316e+00 3.67919e-11 1.89064e-11 ----------------------------------------------------------------------------------------------------- 14 Ti 1 1.800097256733348e+01 1.800097256733077e+01 2.71072e-12 7.56657e-11 2 1.595090522467431e+01 1.595090522467156e+01 2.74447e-12 2.92562e-10 3 6.565326411025654e+00 6.565326411018291e+00 7.36300e-12 9.97167e-11 ----------------------------------------------------------------------------------------------------- 15 O 1 -5.610059134534713e+00 -5.610059134565851e+00 3.11378e-11 5.34107e-10 * 2 -1.473889166543123e+01 -1.473889166544723e+01 1.59925e-11 9.50049e-11 3 -2.601997483797346e+01 -2.601997483796422e+01 9.24416e-12 6.40412e-11 ----------------------------------------------------------------------------------------------------- 16 O 1 -1.147777279256693e+01 -1.147777279255708e+01 9.84102e-12 7.91047e-11 2 4.194253010535163e-01 4.194253010597030e-01 6.18672e-12 5.73478e-11 3 -2.048844559464302e+01 -2.048844559463997e+01 3.05178e-12 1.17527e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 -7.519630145345840e+00 -7.519630145328437e+00 1.74030e-11 1.56875e-10 2 -4.946446205133000e+00 -4.946446205120235e+00 1.27649e-11 9.98925e-11 3 1.427521102402531e+01 1.427521102400803e+01 1.72857e-11 6.43272e-11 ----------------------------------------------------------------------------------------------------- 18 O 1 1.153342111551734e+00 1.153342111577319e+00 2.55846e-11 1.03017e-10 2 -2.340766126243659e+01 -2.340766126244140e+01 4.81393e-12 2.86632e-09 * 3 -8.369134566821034e+00 -8.369134566807086e+00 1.39480e-11 8.61355e-12 ----------------------------------------------------------------------------------------------------- 19 O 1 -5.993534854527534e+00 -5.993534854558203e+00 3.06688e-11 9.25526e-11 2 5.309806416208874e+00 5.309806416206042e+00 2.83151e-12 9.28386e-11 3 -1.627915884749699e+00 -1.627915884752535e+00 2.83618e-12 5.54718e-11 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -9.290487557157954e-01 -9.290487557069135e-01 8.88190e-12 9.31827e-11 2 1.494392662322624e+01 1.494392662325812e+01 3.18874e-11 1.03803e-10 3 1.170303172301947e+01 1.170303172300862e+01 1.08447e-11 1.18339e-10 ----------------------------------------------------------------------------------------------------- 21 O 1 -1.906082454200395e+00 -1.906082454202983e+00 2.58771e-12 1.11807e-10 2 5.934989337403394e+00 5.934989337384149e+00 1.92450e-11 1.32411e-10 3 -6.577639101761443e+00 -6.577639101790999e+00 2.95559e-11 3.41709e-10 ----------------------------------------------------------------------------------------------------- 22 O 1 -7.024533271813866e+00 -7.024533271820130e+00 6.26343e-12 9.44338e-11 2 -4.596412358201214e+00 -4.596412358179002e+00 2.22116e-11 4.37241e-11 3 6.224074490503980e+00 6.224074490473196e+00 3.07843e-11 8.75087e-11 ----------------------------------------------------------------------------------------------------- 23 Ti 1 9.222947395793588e+00 9.222947395795723e+00 2.13518e-12 7.27098e-11 2 -1.180811395308814e+01 -1.180811395307413e+01 1.40155e-11 9.98810e-11 3 1.737350100935942e+00 1.737350100933343e+00 2.59903e-12 1.29221e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.414995990437125e+01 -1.414995990437161e+01 3.62377e-13 1.41675e-10 2 8.066824491400245e-01 8.066824491335125e-01 6.51201e-12 1.58954e-10 3 -1.230004089155233e+00 -1.230004089156094e+00 8.61311e-13 2.22444e-11 ----------------------------------------------------------------------------------------------------- 25 O 1 -7.393157910883371e+00 -7.393157910903029e+00 1.96581e-11 1.03335e-10 2 2.745699609677873e+00 2.745699609694286e+00 1.64126e-11 1.26777e-10 3 -1.013506644553770e+01 -1.013506644554077e+01 3.06422e-12 4.42508e-11 ----------------------------------------------------------------------------------------------------- 26 Ti 1 1.000394402968674e+01 1.000394402968625e+01 4.92051e-13 4.59224e-11 2 -6.066317093006728e-01 -6.066317093245618e-01 2.38890e-11 1.21691e-10 3 2.209181555581210e+01 2.209181555581834e+01 6.23857e-12 2.49791e-11 ----------------------------------------------------------------------------------------------------- 27 O 1 9.135045636728430e+00 9.135045636744954e+00 1.65237e-11 1.07738e-10 2 -9.305356183698203e+00 -9.305356183763449e+00 6.52456e-11 3.33145e-10 3 2.043239058595813e+00 2.043239058661966e+00 6.61533e-11 8.50569e-11 ----------------------------------------------------------------------------------------------------- 28 O 1 -2.230979331682339e+00 -2.230979331664616e+00 1.77232e-11 1.24453e-10 2 7.133492954371190e+00 7.133492954348457e+00 2.27329e-11 7.45350e-11 3 -7.070491215358685e+00 -7.070491215357439e+00 1.24611e-12 6.35048e-12 ----------------------------------------------------------------------------------------------------- 29 O 1 1.202691146313382e+01 1.202691146314873e+01 1.49107e-11 6.35278e-11 2 -9.423111268451006e+00 -9.423111268447483e+00 3.52252e-12 1.99556e-11 3 9.353378124888732e+00 9.353378124925619e+00 3.68878e-11 1.18870e-10 ----------------------------------------------------------------------------------------------------- 30 O 1 6.862891399616450e+00 6.862891399616056e+00 3.94351e-13 6.08109e-11 2 2.264185760929960e+00 2.264185760921829e+00 8.13127e-12 1.71566e-10 3 6.669173648969083e+00 6.669173648958377e+00 1.07052e-11 1.43014e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 9.702250521735820e+00 9.702250521715602e+00 2.02185e-11 1.52797e-10 2 2.369113521319348e+01 2.369113521317648e+01 1.69997e-11 2.17867e-10 3 -1.719037673086942e+00 -1.719037673099782e+00 1.28400e-11 1.37839e-10 ----------------------------------------------------------------------------------------------------- 32 O 1 -5.755559269673086e+00 -5.755559269693130e+00 2.00444e-11 5.69491e-11 2 -4.406782375856682e+00 -4.406782375899046e+00 4.23634e-11 6.81748e-11 3 2.068511806784909e+00 2.068511806789513e+00 4.60387e-12 9.26712e-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 = 2: |F_model - F_numer| error = ----------------------- = 3.93797e-11 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.80933e-10 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 1.80933e-10 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.