!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_KimKimJung_2016_AlTi__MO_618133763375_001 Supported species : Al 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 = Al | a0 = 4.044651031494141 | (Configuration in file "config-Al.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Al 1 3.436525911965789e-01 3.436525911962094e-01 3.69482e-13 8.19425e-11 2 -2.618077135066970e-02 -2.618077134246377e-02 8.20593e-12 1.67646e-09 * 3 3.437088995681828e-02 3.437088997925106e-02 2.24328e-11 2.62628e-09 * ----------------------------------------------------------------------------------------------------- 2 Al 1 -8.101099691017800e-01 -8.101099690966309e-01 5.14910e-12 1.68933e-10 2 8.600115920378795e-01 8.600115920137971e-01 2.40824e-11 1.28895e-10 3 3.127577390207467e-01 3.127577390218406e-01 1.09396e-12 1.17594e-11 ----------------------------------------------------------------------------------------------------- 3 Al 1 -8.242116320851114e-02 -8.242116318379675e-02 2.47144e-11 3.47104e-10 2 -4.844087934567273e-02 -4.844087930977665e-02 3.58961e-11 6.65230e-10 3 -2.547485505583829e-01 -2.547485506184555e-01 6.00726e-11 7.57109e-11 ----------------------------------------------------------------------------------------------------- 4 Al 1 4.983906972712699e-01 4.983906972848873e-01 1.36174e-11 1.02367e-10 2 2.408671156367183e-01 2.408671156298008e-01 6.91744e-12 1.63044e-10 3 3.779437014996986e-01 3.779437014642163e-01 3.54823e-11 4.41837e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 7.931111417768137e-01 7.931111417728764e-01 3.93729e-12 8.10714e-10 2 -3.817072359932426e-01 -3.817072360144325e-01 2.11899e-11 1.56436e-10 3 2.806999037568573e-01 2.806999037432168e-01 1.36405e-11 1.21565e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -3.438254917523603e-01 -3.438254917440494e-01 8.31091e-12 1.20342e-10 2 2.501153026637515e-01 2.501153026677565e-01 4.00496e-12 6.85927e-11 3 3.380287586210458e-01 3.380287586301081e-01 9.06225e-12 1.32820e-09 ----------------------------------------------------------------------------------------------------- 7 Al 1 2.574680736984308e-01 2.574680736849551e-01 1.34757e-11 1.47935e-10 2 -1.219046612242066e+00 -1.219046612262273e+00 2.02074e-11 1.19399e-10 3 -1.651118750217780e+00 -1.651118750225453e+00 7.67275e-12 5.05656e-11 ----------------------------------------------------------------------------------------------------- 8 Al 1 -7.221783476917665e-01 -7.221783476951725e-01 3.40605e-12 1.79328e-10 2 -4.748262701343214e-01 -4.748262701502551e-01 1.59337e-11 2.16145e-10 3 -7.562197728107218e-01 -7.562197727083426e-01 1.02379e-10 1.71668e-10 ----------------------------------------------------------------------------------------------------- 9 Al 1 4.288843075342455e-02 4.288843076266631e-02 9.24176e-12 1.75662e-10 2 -1.188167833067991e+00 -1.188167833071563e+00 3.57181e-12 1.94920e-10 3 -1.184618248272586e+00 -1.184618248282854e+00 1.02685e-11 8.25619e-10 ----------------------------------------------------------------------------------------------------- 10 Al 1 -5.398641278301508e-01 -5.398641278114608e-01 1.86900e-11 4.21000e-11 2 4.980765562423825e-01 4.980765562427282e-01 3.45723e-13 4.01855e-09 * 3 -7.222686140810005e-01 -7.222686140815989e-01 5.98410e-13 2.63556e-10 ----------------------------------------------------------------------------------------------------- 11 Al 1 -3.572753881359405e-01 -3.572753881240897e-01 1.18508e-11 2.49441e-10 2 -8.581020031994876e-01 -8.581020032398190e-01 4.03314e-11 9.57195e-10 3 7.845981306438090e-01 7.845981306785337e-01 3.47247e-11 3.09379e-09 * ----------------------------------------------------------------------------------------------------- 12 Al 1 2.596028907967807e-02 2.596028908163867e-02 1.96061e-12 5.06429e-10 2 1.245097728346232e+00 1.245097728349032e+00 2.79976e-12 2.40915e-10 3 7.763446163722213e-01 7.763446163819094e-01 9.68814e-12 1.22900e-10 ----------------------------------------------------------------------------------------------------- 13 Al 1 -5.365341876815753e-01 -5.365341876619382e-01 1.96372e-11 4.49160e-09 * 2 -1.200162143003767e+00 -1.200162142991066e+00 1.27003e-11 1.19191e-10 3 -1.957550015823236e+00 -1.957550015840928e+00 1.76912e-11 7.40812e-10 ----------------------------------------------------------------------------------------------------- 14 Al 1 8.988775541241351e-02 8.988775541787836e-02 5.46485e-12 1.17706e-10 2 4.855436320620268e-01 4.855436320565927e-01 5.43404e-12 3.38328e-11 3 -1.387144392266403e-01 -1.387144392390289e-01 1.23885e-11 3.84984e-09 * ----------------------------------------------------------------------------------------------------- 15 Al 1 1.761450954861486e+00 1.761450955001501e+00 1.40015e-10 9.01355e-11 2 -6.436069113377252e-01 -6.436069114161607e-01 7.84355e-11 1.15220e-10 3 7.520276859211168e-01 7.520276858964825e-01 2.46343e-11 4.92523e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 5.978494647491811e-01 5.978494647608829e-01 1.17018e-11 9.09575e-10 2 1.336599645526329e+00 1.336599645525806e+00 5.22471e-13 2.55522e-10 3 8.753612998807425e-01 8.753612999025504e-01 2.18079e-11 2.67637e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 4.232924879699108e-01 4.232924879359532e-01 3.39576e-11 6.89677e-11 2 3.604714258365112e-01 3.604714258296253e-01 6.88588e-12 3.47143e-10 3 -9.557916874994031e-02 -9.557916875452310e-02 4.58279e-12 1.08105e-11 ----------------------------------------------------------------------------------------------------- 18 Al 1 -5.049839872936553e-01 -5.049839872641195e-01 2.95358e-11 1.04749e-09 2 4.028593471328348e-01 4.028593472490811e-01 1.16246e-10 2.27078e-10 3 1.019487429191001e+00 1.019487429153297e+00 3.77036e-11 1.90332e-09 * ----------------------------------------------------------------------------------------------------- 19 Al 1 2.575143922018392e-01 2.575143922074541e-01 5.61495e-12 1.75903e-10 2 3.794699165459633e-01 3.794699165730738e-01 2.71104e-11 2.93275e-10 3 -4.713117181409814e-01 -4.713117181136346e-01 2.73468e-11 2.32075e-10 ----------------------------------------------------------------------------------------------------- 20 Al 1 4.062913644585930e-01 4.062913644644764e-01 5.88335e-12 4.80885e-11 2 3.113003992267839e-01 3.113003992204914e-01 6.29252e-12 1.62568e-10 3 -4.575010808376562e-01 -4.575010808420337e-01 4.37755e-12 4.64536e-11 ----------------------------------------------------------------------------------------------------- 21 Al 1 -9.520288286595396e-01 -9.520288286466931e-01 1.28465e-11 2.24339e-10 2 4.430035600900081e-02 4.430035607024969e-02 6.12489e-11 1.92895e-10 3 8.201315241913862e-01 8.201315242197195e-01 2.83332e-11 7.00061e-11 ----------------------------------------------------------------------------------------------------- 22 Al 1 2.873278695623234e-01 2.873278695771740e-01 1.48506e-11 6.94753e-11 2 1.511178729448910e+00 1.511178729463908e+00 1.49980e-11 1.22733e-10 3 1.447152316912314e+00 1.447152316861451e+00 5.08629e-11 7.78415e-11 ----------------------------------------------------------------------------------------------------- 23 Al 1 -3.449440560560186e-01 -3.449440560282424e-01 2.77762e-11 2.42792e-10 2 3.006117704353070e-01 3.006117704179175e-01 1.73894e-11 1.44226e-10 3 -3.734060708052642e-01 -3.734060707940492e-01 1.12150e-11 8.28368e-11 ----------------------------------------------------------------------------------------------------- 24 Al 1 7.546372080369666e-02 7.546372079054926e-02 1.31474e-11 1.30407e-10 2 -5.937016491823286e-04 -5.937016283486261e-04 2.08337e-11 1.91243e-10 3 -6.192852818154609e-01 -6.192852818132848e-01 2.17615e-12 4.35813e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -3.619449613179131e-01 -3.619449612781924e-01 3.97207e-11 1.02934e-10 2 -8.543636737279424e-01 -8.543636737195484e-01 8.39406e-12 1.65954e-10 3 2.198724703597425e-01 2.198724704145963e-01 5.48537e-11 1.54118e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 -4.995059878592494e-01 -4.995059878823544e-01 2.31050e-11 6.46032e-11 2 1.019971309665033e+00 1.019971309705319e+00 4.02858e-11 1.45177e-10 3 -7.917960883788592e-01 -7.917960883524611e-01 2.63981e-11 4.49545e-10 ----------------------------------------------------------------------------------------------------- 27 Al 1 5.695347882850870e-01 5.695347883580123e-01 7.29253e-11 3.99764e-10 2 -2.394436846487052e+00 -2.394436846557656e+00 7.06044e-11 6.98572e-10 3 7.839688761011113e-01 7.839688760887314e-01 1.23799e-11 8.34128e-10 ----------------------------------------------------------------------------------------------------- 28 Al 1 -5.446234038934674e-01 -5.446234038991056e-01 5.63816e-12 2.84434e-10 2 6.944340251598240e-01 6.944340251942368e-01 3.44128e-11 4.67588e-10 3 -2.318279184599022e-01 -2.318279184578473e-01 2.05491e-12 3.27607e-11 ----------------------------------------------------------------------------------------------------- 29 Al 1 -2.440918629055693e-01 -2.440918630001892e-01 9.46200e-11 1.60358e-10 2 -7.057629502897574e-01 -7.057629502342896e-01 5.54679e-11 3.05303e-10 3 6.755891576608803e-01 6.755891576235398e-01 3.73406e-11 3.12854e-10 ----------------------------------------------------------------------------------------------------- 30 Al 1 -7.998225684720663e-02 -7.998225681942232e-02 2.77843e-11 1.07874e-10 2 6.365060183912106e-01 6.365060183865143e-01 4.69624e-12 2.07176e-10 3 -3.994794171810697e-01 -3.994794171559157e-01 2.51539e-11 2.15582e-09 * ----------------------------------------------------------------------------------------------------- 31 Al 1 -7.196129164542195e-02 -7.196129167388413e-02 2.84622e-11 8.12897e-10 2 -9.584853879201196e-01 -9.584853879101891e-01 9.93050e-12 2.37149e-10 3 4.908346456816607e-01 4.908346456861971e-01 4.53632e-12 1.73409e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 5.661912897993999e-01 5.661912898348114e-01 3.54115e-11 1.42812e-10 2 3.764683493822977e-01 3.764683494010944e-01 1.87967e-11 2.02828e-10 3 1.162559895883294e-01 1.162559895780405e-01 1.02889e-11 2.41228e-09 * ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 24, direction = 2: |F_model - F_numer| error = ----------------------- = 3.50912e-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. 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 7.675625885449386e-01 7.675625885408411e-01 4.09750e-12 5.93398e-11 2 5.653083814092233e-01 5.653083814099492e-01 7.25864e-13 1.06088e-09 3 3.355336565239141e-01 3.355336565247672e-01 8.53095e-13 1.02488e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -6.046515951047416e-01 -6.046515951212071e-01 1.64655e-11 1.41148e-10 2 -6.414408390919082e-01 -6.414408390826715e-01 9.23672e-12 1.76507e-11 3 9.462278716192620e-01 9.462278716144953e-01 4.76674e-12 4.53906e-11 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.585147782426391e-01 -1.585147782395050e-01 3.13408e-12 5.51659e-11 2 6.776333686783985e-01 6.776333686355488e-01 4.28497e-11 6.87904e-11 3 -7.552122161723959e-01 -7.552122161612174e-01 1.11785e-11 7.73407e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 4.225071337955756e-01 4.225071337955223e-01 5.33462e-14 7.74442e-11 2 3.574328974834684e-01 3.574328974814438e-01 2.02460e-12 2.77734e-10 3 -9.030874799349077e-01 -9.030874799431367e-01 8.22897e-12 2.74496e-09 * ----------------------------------------------------------------------------------------------------- 5 Ti 1 -5.239383796809076e-01 -5.239383796816119e-01 7.04325e-13 5.82470e-10 2 -5.104107915266056e-01 -5.104107915009476e-01 2.56580e-11 3.21193e-11 3 -4.581405485363321e-01 -4.581405485072853e-01 2.90469e-11 3.16143e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 6.110242735233143e-01 6.110242735104684e-01 1.28459e-11 6.70087e-11 2 4.025323023576271e-01 4.025323023393935e-01 1.82336e-11 1.70211e-10 3 -9.366119868537870e-01 -9.366119868545307e-01 7.43738e-13 3.74437e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 1.100177336290097e+00 1.100177336364834e+00 7.47364e-11 1.39892e-10 2 -1.447184673629863e+00 -1.447184673613987e+00 1.58757e-11 1.08796e-10 3 7.872401140199619e-01 7.872401140253440e-01 5.38214e-12 1.56146e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -1.430355026262907e+00 -1.430355026177872e+00 8.50355e-11 3.77926e-10 2 1.535732200610306e+00 1.535732200633030e+00 2.27245e-11 8.51177e-11 3 6.032609886603527e-01 6.032609887104059e-01 5.00532e-11 2.70267e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 5.930062181691036e-01 5.930062181650825e-01 4.02112e-12 4.28784e-11 2 -7.656242553726924e-03 -7.656242556391096e-03 2.66417e-12 5.61501e-11 3 6.178200094001355e-01 6.178200094072880e-01 7.15250e-12 5.81689e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -2.977049958136025e-01 -2.977049957758020e-01 3.78006e-11 1.00368e-10 2 -1.385981165917059e-01 -1.385981166203557e-01 2.86498e-11 3.32076e-11 3 -1.343967066075090e-01 -1.343967066206056e-01 1.30966e-11 7.70445e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -1.305032988191632e+00 -1.305032988157967e+00 3.36646e-11 6.37408e-11 2 1.150066372552321e+00 1.150066372638968e+00 8.66478e-11 2.89393e-10 3 -1.638350043593011e+00 -1.638350043603481e+00 1.04701e-11 4.73093e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 4.193721032087573e-01 4.193721031735171e-01 3.52401e-11 1.68066e-10 2 -3.154081492977271e-01 -3.154081492871789e-01 1.05482e-11 3.30719e-11 3 -3.065431567162785e-01 -3.065431566854339e-01 3.08446e-11 7.68977e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -1.019880444936389e+00 -1.019880444945987e+00 9.59854e-12 3.53155e-11 2 -5.165678775687155e-01 -5.165678775476943e-01 2.10212e-11 2.02822e-10 3 3.222940911527363e-01 3.222940911648206e-01 1.20843e-11 2.88376e-11 ----------------------------------------------------------------------------------------------------- 14 Ti 1 1.269618160368051e+00 1.269618160345973e+00 2.20777e-11 4.40032e-11 2 1.215980578466699e+00 1.215980578486209e+00 1.95091e-11 8.56386e-11 3 -6.457940064302596e-01 -6.457940064358271e-01 5.56744e-12 1.12277e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -5.309973575427079e-02 -5.309973581107397e-02 5.68032e-11 6.49200e-09 * 2 -7.423017548445154e-01 -7.423017548145379e-01 2.99776e-11 1.20620e-10 3 -3.643241636649740e-01 -3.643241636674622e-01 2.48823e-12 4.52063e-11 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -8.092547973422598e-01 -8.092547973482921e-01 6.03229e-12 4.64949e-11 2 -5.906007338407572e-01 -5.906007338776973e-01 3.69401e-11 4.40273e-11 3 9.750854738958082e-01 9.750854738941966e-01 1.61160e-12 1.36507e-09 * ----------------------------------------------------------------------------------------------------- 17 Ti 1 3.776984393445087e-01 3.776984393673249e-01 2.28162e-11 1.76268e-09 * 2 -1.016087286686854e+00 -1.016087286685126e+00 1.72728e-12 5.18878e-11 3 -9.863755569438241e-01 -9.863755569281831e-01 1.56409e-11 7.26315e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 3.213994614527348e-01 3.213994614483203e-01 4.41452e-12 1.51193e-10 2 -7.953909859407406e-01 -7.953909859426392e-01 1.89859e-12 8.19004e-11 3 6.333642799704619e-01 6.333642799582994e-01 1.21625e-11 2.59401e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -5.680176940844611e-02 -5.680176945968515e-02 5.12390e-11 5.64518e-10 2 -5.251123775893469e-01 -5.251123776047917e-01 1.54448e-11 4.73803e-10 3 4.090962403556263e-01 4.090962403504632e-01 5.16315e-12 2.13112e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -4.932840977183899e-01 -4.932840976895808e-01 2.88091e-11 2.02590e-10 2 1.457741781110795e+00 1.457741781115596e+00 4.80105e-12 6.76365e-10 3 1.159746664933978e+00 1.159746664926431e+00 7.54730e-12 5.75984e-11 ----------------------------------------------------------------------------------------------------- 21 Ti 1 1.469091031997613e-01 1.469091031662536e-01 3.35077e-11 4.28239e-10 2 -7.372504310187383e-01 -7.372504309970104e-01 2.17280e-11 2.08754e-10 3 -5.162906262183938e-01 -5.162906261539305e-01 6.44633e-11 7.49972e-11 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -1.341534662528259e+00 -1.341534662407821e+00 1.20438e-10 2.93511e-10 2 -1.258207530193151e+00 -1.258207530178493e+00 1.46576e-11 1.45856e-10 3 7.195015723632806e-01 7.195015723456331e-01 1.76476e-11 1.01621e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 3.840913836309059e-01 3.840913836492206e-01 1.83147e-11 2.95900e-10 2 1.048018983664947e-01 1.048018983990756e-01 3.25809e-11 4.60610e-10 3 2.876302960563356e-01 2.876302960534576e-01 2.87798e-12 1.52406e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 8.379712591102914e-01 8.379712592498793e-01 1.39588e-10 2.04947e-10 2 5.693268360491834e-01 5.693268361183839e-01 6.92004e-11 2.20028e-08 * 3 -5.636578168152394e-01 -5.636578167598905e-01 5.53489e-11 1.29134e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.589930440914477e+00 -1.589930440915899e+00 1.42286e-12 5.41156e-11 2 -1.077809369203738e+00 -1.077809369218390e+00 1.46516e-11 9.48159e-11 3 4.410285875852481e-01 4.410285875646457e-01 2.06024e-11 4.40093e-11 ----------------------------------------------------------------------------------------------------- 26 Ti 1 7.294682287086235e-01 7.294682287025341e-01 6.08935e-12 1.26118e-10 2 -3.436501674475735e-02 -3.436501676403740e-02 1.92800e-11 1.18243e-10 3 3.997985207708011e-01 3.997985207550921e-01 1.57090e-11 9.94549e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -5.528915248922370e-01 -5.528915248839417e-01 8.29536e-12 2.49993e-10 2 7.658195023387051e-01 7.658195023017479e-01 3.69572e-11 2.26217e-10 3 -5.012627081001851e-01 -5.012627081147536e-01 1.45685e-11 1.26421e-09 ----------------------------------------------------------------------------------------------------- 28 Ti 1 7.504886027379343e-01 7.504886027318285e-01 6.10578e-12 4.16449e-10 2 -4.136910032531682e-01 -4.136910032503395e-01 2.82874e-12 2.26751e-11 3 -4.914555709368151e-01 -4.914555709229277e-01 1.38874e-11 4.20422e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 1.447392307215057e+00 1.447392307219771e+00 4.71467e-12 8.25293e-09 * 2 1.839812682214394e+00 1.839812682227622e+00 1.32274e-11 3.46625e-11 3 5.107524556221559e-01 5.107524556314268e-01 9.27092e-12 3.07525e-11 ----------------------------------------------------------------------------------------------------- 30 Ti 1 2.603691123465020e-01 2.603691123600412e-01 1.35392e-11 3.89102e-10 2 3.469927284878026e-01 3.469927285264689e-01 3.86663e-11 1.89974e-10 3 6.295552206039265e-01 6.295552206014821e-01 2.44449e-12 3.23249e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -2.170416852389117e-01 -2.170416852295851e-01 9.32660e-12 3.02499e-09 * 2 1.401860182038282e-01 1.401860182062181e-01 2.38984e-12 8.75186e-10 3 -1.509477186036264e-01 -1.509477186223598e-01 1.87334e-11 8.97040e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 1.486121038391439e-02 1.486121037944246e-02 4.47192e-12 3.79739e-10 2 -3.612843687532289e-01 -3.612843688036861e-01 5.04572e-11 2.80145e-09 * 3 -4.254857374064451e-01 -4.254857373975231e-01 8.92203e-12 5.57979e-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 = 19, direction = 1: |F_model - F_numer| error = ----------------------- = 9.02068e-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 = Al Ti | a0 = 4.054133614767579 | (Configuration in file "config-AlTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 -1.579738613289648e+00 -1.579738613274946e+00 1.47014e-11 1.12846e-10 2 -5.739124667358767e-01 -5.739124667383417e-01 2.46503e-12 2.41132e-11 3 -1.828939380595599e+00 -1.828939380592082e+00 3.51763e-12 1.84079e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -4.121232189552413e+00 -4.121232189534649e+00 1.77636e-11 6.33165e-10 2 4.173999332243118e+00 4.173999332221471e+00 2.16467e-11 2.74579e-10 3 -1.777862028306120e+00 -1.777862028289062e+00 1.70577e-11 1.51825e-10 ----------------------------------------------------------------------------------------------------- 3 Al 1 1.132146214660629e+00 1.132146214669765e+00 9.13514e-12 1.63654e-10 2 -1.243473263955484e+00 -1.243473263983015e+00 2.75302e-11 9.53526e-12 3 3.116807708231650e+00 3.116807708218092e+00 1.35580e-11 3.30608e-10 ----------------------------------------------------------------------------------------------------- 4 Al 1 2.910386884987931e-01 2.910386885165092e-01 1.77161e-11 1.14655e-10 2 4.437348282084584e-01 4.437348282181708e-01 9.71240e-12 1.95736e-10 3 7.459759533585129e-01 7.459759533611284e-01 2.61557e-12 8.68032e-11 ----------------------------------------------------------------------------------------------------- 5 Al 1 2.955067321440380e+00 2.955067321427638e+00 1.27418e-11 1.01251e-10 2 -2.639964279015721e+00 -2.639964278994793e+00 2.09273e-11 2.97540e-11 3 -2.856310823646482e-01 -2.856310823927656e-01 2.81174e-11 3.58763e-10 ----------------------------------------------------------------------------------------------------- 6 Al 1 -1.092851120213208e-01 -1.092851120290458e-01 7.72504e-12 4.48242e-10 2 -1.826566186619824e-01 -1.826566186935628e-01 3.15804e-11 7.93212e-10 3 5.111927833076104e-01 5.111927833110262e-01 3.41582e-12 2.08689e-12 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -3.008437434601159e-01 -3.008437434448503e-01 1.52656e-11 6.58082e-11 2 9.181407352448248e-01 9.181407353091099e-01 6.42851e-11 1.01680e-10 3 3.469831643050488e-01 3.469831643633243e-01 5.82754e-11 9.62901e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.626314072755762e+00 1.626314072796747e+00 4.09857e-11 7.66918e-10 2 -1.732497853504449e+00 -1.732497853504697e+00 2.47358e-13 3.81647e-10 3 3.320412811311080e+00 3.320412811355092e+00 4.40119e-11 3.75001e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 3.110879886170992e-03 3.110879854742803e-03 3.14282e-11 5.94736e-11 2 -6.308364326981416e-01 -6.308364326738994e-01 2.42422e-11 4.67307e-11 3 -9.366321079119705e-01 -9.366321079032337e-01 8.73679e-12 2.49739e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 5.441935015856179e-01 5.441935015885335e-01 2.91567e-12 1.70978e-09 * 2 -3.087873619513445e-01 -3.087873619383636e-01 1.29809e-11 1.96695e-09 * 3 2.563226062342244e-01 2.563226062358707e-01 1.64629e-12 7.44484e-11 ----------------------------------------------------------------------------------------------------- 11 Al 1 1.348439671708725e+00 1.348439671687406e+00 2.13196e-11 3.34547e-10 2 -1.200371117723958e+00 -1.200371117675613e+00 4.83453e-11 2.04063e-10 3 -6.359096974718136e-02 -6.359096971541435e-02 3.17670e-11 3.06381e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -1.022684184477153e+00 -1.022684184473363e+00 3.78964e-12 1.11540e-09 2 1.152681888427758e+00 1.152681888553534e+00 1.25777e-10 1.41368e-10 3 2.544080409772114e-01 2.544080409770174e-01 1.94067e-13 1.59270e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 6.084689921585172e-01 6.084689921548678e-01 3.64941e-12 2.06244e-10 2 2.544119840280764e+00 2.544119840259640e+00 2.11240e-11 1.29733e-10 3 -6.523697379317699e-01 -6.523697379250402e-01 6.72973e-12 5.91348e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -8.181187949181534e-01 -8.181187949125122e-01 5.64127e-12 5.17841e-11 2 -1.067217540224307e+00 -1.067217540218200e+00 6.10623e-12 1.06266e-10 3 9.150930023972672e-01 9.150930024040167e-01 6.74949e-12 5.59881e-11 ----------------------------------------------------------------------------------------------------- 15 Al 1 -9.101107462670012e-01 -9.101107462166613e-01 5.03398e-11 6.92873e-10 2 1.204720477247895e+00 1.204720477237795e+00 1.01004e-11 1.16512e-10 3 -9.599620633474522e-01 -9.599620633025282e-01 4.49240e-11 6.22753e-10 ----------------------------------------------------------------------------------------------------- 16 Al 1 3.064533450826447e-01 3.064533451205755e-01 3.79308e-11 6.19322e-11 2 1.001538006790076e+00 1.001538006724575e+00 6.55009e-11 2.96251e-10 3 -2.055810247714104e+00 -2.055810247722841e+00 8.73701e-12 1.65300e-10 ----------------------------------------------------------------------------------------------------- 17 Al 1 6.336650646643075e-01 6.336650646552903e-01 9.01723e-12 1.69405e-10 2 5.365021011996035e-01 5.365021012027175e-01 3.11395e-12 9.21472e-11 3 4.734639770151335e-01 4.734639770084771e-01 6.65640e-12 3.15557e-10 ----------------------------------------------------------------------------------------------------- 18 Al 1 -1.445404159005743e-01 -1.445404158933449e-01 7.22947e-12 6.28222e-09 * 2 -3.979424204033311e+00 -3.979424204006206e+00 2.71045e-11 5.77687e-10 3 -2.836814946078333e+00 -2.836814946168865e+00 9.05311e-11 4.15489e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -8.126094343788302e-01 -8.126094343374326e-01 4.13976e-11 2.15590e-09 * 2 -3.210695367900950e-01 -3.210695367367223e-01 5.33727e-11 5.67306e-11 3 -6.274844705586524e-01 -6.274844705577047e-01 9.47686e-13 2.01261e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.587048551544503e-01 -1.587048551630121e-01 8.56182e-12 4.06637e-11 2 -6.768624542281928e-01 -6.768624542294066e-01 1.21381e-12 1.36443e-09 * 3 -6.388771017839606e-01 -6.388771017438082e-01 4.01524e-11 1.95872e-09 * ----------------------------------------------------------------------------------------------------- 21 Al 1 -9.861648806004580e-01 -9.861648806151856e-01 1.47276e-11 1.58113e-10 2 6.594883591759961e-01 6.594883591283336e-01 4.76625e-11 1.01914e-10 3 -8.579240364488635e-01 -8.579240365894986e-01 1.40635e-10 1.87320e-10 ----------------------------------------------------------------------------------------------------- 22 Al 1 -5.989807794153758e-01 -5.989807794415355e-01 2.61597e-11 3.59954e-11 2 -1.065607615262547e+00 -1.065607615286832e+00 2.42852e-11 2.20362e-10 3 1.433842155493084e-01 1.433842154473264e-01 1.01982e-10 2.76434e-11 ----------------------------------------------------------------------------------------------------- 23 Al 1 3.200470911208279e-01 3.200470911110164e-01 9.81143e-12 2.97602e-11 2 3.556764425264579e-01 3.556764425178348e-01 8.62305e-12 1.39723e-10 3 2.463496119248922e-01 2.463496119109100e-01 1.39822e-11 4.15271e-09 * ----------------------------------------------------------------------------------------------------- 24 Al 1 1.067978387218879e+00 1.067978387202936e+00 1.59428e-11 3.67931e-09 * 2 9.995119139326506e-01 9.995119139320838e-01 5.66769e-13 1.76854e-10 3 -6.168070427550613e-01 -6.168070428697665e-01 1.14705e-10 2.88579e-10 ----------------------------------------------------------------------------------------------------- 25 Al 1 -2.470907744949368e+00 -2.470907744924503e+00 2.48650e-11 2.10799e-10 2 -9.479612335253893e-01 -9.479612335627908e-01 3.74015e-11 1.56092e-09 * 3 -8.627123446365097e-01 -8.627123445613003e-01 7.52094e-11 1.82637e-10 ----------------------------------------------------------------------------------------------------- 26 Al 1 1.721351586896253e+00 1.721351586882808e+00 1.34457e-11 3.00950e-10 2 1.417092651619854e+00 1.417092651608562e+00 1.12914e-11 1.58464e-11 3 -2.399923035701241e-01 -2.399923035578051e-01 1.23191e-11 2.45864e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 1.688278332544277e+00 1.688278332540752e+00 3.52540e-12 1.22861e-08 * 2 2.756319546218479e+00 2.756319546392523e+00 1.74044e-10 8.39956e-10 3 3.624788155477438e+00 3.624788155524593e+00 4.71552e-11 7.08820e-11 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -6.173552935457014e-01 -6.173552935542624e-01 8.56104e-12 5.97956e-11 2 1.899722669233366e-01 1.899722669315375e-01 8.20091e-12 3.78014e-11 3 6.681563863083910e-01 6.681563862949098e-01 1.34812e-11 8.36082e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 8.778254873252705e-01 8.778254872971882e-01 2.80823e-11 3.77305e-10 2 -1.503738135028270e+00 -1.503738135068760e+00 4.04894e-11 4.77123e-11 3 5.387615061131580e-01 5.387615061468298e-01 3.36718e-11 3.06831e-11 ----------------------------------------------------------------------------------------------------- 30 Ti 1 1.060938401454140e+00 1.060938401470394e+00 1.62539e-11 6.33085e-11 2 1.144611626035662e+00 1.144611625956515e+00 7.91462e-11 1.27075e-10 3 -2.073224562038935e+00 -2.073224561983782e+00 5.51528e-11 1.81055e-09 * ----------------------------------------------------------------------------------------------------- 31 Ti 1 -2.161363867372010e-01 -2.161363867335236e-01 3.67736e-12 1.99964e-09 * 2 -1.176264422440079e+00 -1.176264422405496e+00 3.45828e-11 3.11690e-10 3 8.829663117113115e-01 8.829663117250641e-01 1.37527e-11 1.58211e-10 ----------------------------------------------------------------------------------------------------- 32 Al 1 -1.317903864333431e+00 -1.317903864346625e+00 1.31932e-11 2.05984e-10 2 -2.474654802957851e-01 -2.474654802909727e-01 4.81240e-12 8.18411e-11 3 1.269568191567045e+00 1.269568191571530e+00 4.48508e-12 1.01950e-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 = 9, direction = 1: |F_model - F_numer| error = ----------------------- = 1.01027e-08 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 3.50912e-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 3.50912e-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.