!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : Tersoff_LAMMPS_Nord_Albe_Erhart_Nordlund_GaN__MO_612061685362_001 Supported species : Ga N 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 = Ga | a0 = 3.9710893631 | (Configuration in file "config-Ga.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ga 1 6.089485951165580e+00 6.089485951164437e+00 1.14309e-12 2.41283e-11 2 2.691953275397358e+00 2.691953275398288e+00 9.29923e-13 1.02367e-11 3 2.510907937519863e+00 2.510907937518400e+00 1.46239e-12 1.28353e-10 ----------------------------------------------------------------------------------------------------- 2 Ga 1 -2.569437033826238e+00 -2.569437033818971e+00 7.26752e-12 9.95959e-11 2 -1.498537171250815e+00 -1.498537171253335e+00 2.52021e-12 8.49654e-12 3 3.221179908937728e+00 3.221179908942476e+00 4.74820e-12 4.31903e-11 ----------------------------------------------------------------------------------------------------- 3 Ga 1 -2.025555993868570e+00 -2.025555993866460e+00 2.11076e-12 2.89142e-11 2 2.728750936193538e+00 2.728750936192698e+00 8.39773e-13 3.07954e-11 3 -5.025870094179340e+00 -5.025870094176662e+00 2.67786e-12 1.64100e-09 * ----------------------------------------------------------------------------------------------------- 4 Ga 1 3.874855880907669e+00 3.874855880901754e+00 5.91482e-12 2.07638e-11 2 6.956503143757736e-01 6.956503143830259e-01 7.25231e-12 8.07965e-12 3 1.104124705111901e+00 1.104124705109869e+00 2.03193e-12 1.63143e-11 ----------------------------------------------------------------------------------------------------- 5 Ga 1 3.937306088788125e-01 3.937306088742697e-01 4.54281e-12 2.17691e-11 2 2.349765825286537e+00 2.349765825284699e+00 1.83720e-12 4.59472e-11 3 3.564516535253337e+00 3.564516535261189e+00 7.85150e-12 1.94373e-11 ----------------------------------------------------------------------------------------------------- 6 Ga 1 -3.293247047549654e+00 -3.293247047553758e+00 4.10472e-12 4.67555e-11 2 -1.002293161314599e+00 -1.002293161320722e+00 6.12332e-12 4.62763e-11 3 1.466878728997702e+00 1.466878729008842e+00 1.11406e-11 2.89566e-11 ----------------------------------------------------------------------------------------------------- 7 Ga 1 -7.681997212229549e-01 -7.681997212164686e-01 6.48626e-12 3.42599e-11 2 -7.011845005040819e-01 -7.011845005043659e-01 2.83995e-13 2.31379e-11 3 -2.566297805541177e+00 -2.566297805538584e+00 2.59304e-12 2.82743e-11 ----------------------------------------------------------------------------------------------------- 8 Ga 1 -1.267251589120546e+00 -1.267251589114316e+00 6.23035e-12 2.06168e-10 * 2 -1.592428312632254e+00 -1.592428312638702e+00 6.44795e-12 7.52149e-11 3 -5.976337332814229e-01 -5.976337332831536e-01 1.73073e-12 1.07963e-10 ----------------------------------------------------------------------------------------------------- 9 Ga 1 -2.749303193545876e-01 -2.749303193498228e-01 4.76480e-12 3.03769e-10 * 2 -1.786512596637745e+00 -1.786512596654104e+00 1.63589e-11 1.38547e-10 3 2.000713265438887e+00 2.000713265443310e+00 4.42313e-12 1.44187e-11 ----------------------------------------------------------------------------------------------------- 10 Ga 1 -1.637199452346415e+00 -1.637199452338872e+00 7.54241e-12 3.48936e-11 2 -5.756025725901184e-01 -5.756025725894028e-01 7.15539e-13 3.94439e-11 3 2.073838104652351e+00 2.073838104653459e+00 1.10845e-12 1.08114e-11 ----------------------------------------------------------------------------------------------------- 11 Ga 1 -1.264702641297901e+00 -1.264702641321826e+00 2.39251e-11 9.31339e-11 2 -2.185087836852617e+00 -2.185087836851331e+00 1.28653e-12 4.98050e-11 3 -1.193521107580734e+00 -1.193521107572720e+00 8.01403e-12 5.05307e-12 ----------------------------------------------------------------------------------------------------- 12 Ga 1 2.857736513083190e+00 2.857736513079281e+00 3.90887e-12 5.17928e-11 2 -8.933501549354500e-01 -8.933501549345990e-01 8.50986e-13 7.33613e-12 3 -2.155068251451980e+00 -2.155068251442007e+00 9.97291e-12 2.49973e-11 ----------------------------------------------------------------------------------------------------- 13 Ga 1 -1.054032651279651e+00 -1.054032651284431e+00 4.77995e-12 3.18063e-11 2 2.118207367556046e-01 2.118207367607313e-01 5.12670e-12 2.85228e-11 3 -2.386148421989096e+00 -2.386148421988833e+00 2.63789e-13 2.44773e-11 ----------------------------------------------------------------------------------------------------- 14 Ga 1 -9.861808454800215e-01 -9.861808454835927e-01 3.57125e-12 1.46569e-11 2 -3.275254270671135e-01 -3.275254270678635e-01 7.49956e-13 1.04042e-11 3 9.034719129587726e-01 9.034719129612714e-01 2.49878e-12 3.50042e-12 ----------------------------------------------------------------------------------------------------- 15 Ga 1 2.352681575509349e+00 2.352681575506537e+00 2.81153e-12 1.75038e-11 2 4.824681461122181e-01 4.824681461113418e-01 8.76299e-13 2.62115e-11 3 2.621151176823374e+00 2.621151176820324e+00 3.04912e-12 5.07727e-12 ----------------------------------------------------------------------------------------------------- 16 Ga 1 2.308569029269381e+00 2.308569029267108e+00 2.27285e-12 9.64384e-11 2 5.997487533244470e-01 5.997487533246486e-01 2.01617e-13 8.13505e-12 3 1.213988889248603e-01 1.213988889126967e-01 1.21636e-11 1.00266e-10 ----------------------------------------------------------------------------------------------------- 17 Ga 1 1.241981811208307e+00 1.241981811206692e+00 1.61493e-12 9.15417e-11 2 2.046125626799542e+00 2.046125626802828e+00 3.28626e-12 2.81735e-11 3 -1.810732341989232e+00 -1.810732341985538e+00 3.69327e-12 5.88796e-11 ----------------------------------------------------------------------------------------------------- 18 Ga 1 -1.789855045301898e+00 -1.789855045301208e+00 6.90559e-13 7.21623e-12 2 -9.091478230185478e-01 -9.091478230120401e-01 6.50768e-12 7.07755e-11 3 2.092418287842368e+00 2.092418287843707e+00 1.33893e-12 1.92979e-11 ----------------------------------------------------------------------------------------------------- 19 Ga 1 3.061557646183125e+00 3.061557646179935e+00 3.19078e-12 2.53024e-11 2 1.323783406172853e+00 1.323783406168717e+00 4.13602e-12 5.63105e-12 3 -1.773828836742652e+00 -1.773828836740646e+00 2.00617e-12 1.17277e-11 ----------------------------------------------------------------------------------------------------- 20 Ga 1 2.118274507856500e+00 2.118274507854447e+00 2.05258e-12 1.12927e-11 2 1.005673711840269e-01 1.005673711848871e-01 8.60187e-13 4.06468e-12 3 -2.129880401201755e+00 -2.129880401200300e+00 1.45484e-12 1.51963e-11 ----------------------------------------------------------------------------------------------------- 21 Ga 1 -3.925343763204285e+00 -3.925343763211706e+00 7.42073e-12 1.77542e-11 2 4.217455439531181e+00 4.217455439528726e+00 2.45581e-12 3.29994e-11 3 5.158725354356680e+00 5.158725354358311e+00 1.63158e-12 1.64536e-10 * ----------------------------------------------------------------------------------------------------- 22 Ga 1 -7.411484307880437e-01 -7.411484307809569e-01 7.08678e-12 4.37609e-11 2 1.689117519512592e+00 1.689117519511717e+00 8.75078e-13 3.42673e-11 3 -3.891953502799521e-01 -3.891953502740699e-01 5.88218e-12 1.45252e-11 ----------------------------------------------------------------------------------------------------- 23 Ga 1 -3.300861143557937e+00 -3.300861143552501e+00 5.43610e-12 8.80984e-12 2 2.202171525060455e+00 2.202171525058172e+00 2.28217e-12 1.17368e-11 3 -8.906648892247451e-01 -8.906648892254450e-01 6.99885e-13 5.69234e-12 ----------------------------------------------------------------------------------------------------- 24 Ga 1 3.502135222910082e+00 3.502135222907715e+00 2.36655e-12 1.25784e-11 2 -2.605986567072113e+00 -2.605986567068972e+00 3.14060e-12 7.00018e-12 3 -4.337842428503452e+00 -4.337842428503404e+00 4.88498e-14 9.25926e-12 ----------------------------------------------------------------------------------------------------- 25 Ga 1 2.227317753156592e+00 2.227317753149925e+00 6.66756e-12 2.15352e-11 2 -2.009053149866906e+00 -2.009053149867173e+00 2.67342e-13 1.68390e-11 3 1.719842706218591e+00 1.719842706215089e+00 3.50209e-12 7.25053e-11 ----------------------------------------------------------------------------------------------------- 26 Ga 1 -1.669480546677911e+00 -1.669480546670226e+00 7.68541e-12 2.92484e-11 2 2.684809198319646e-01 2.684809198308473e-01 1.11727e-12 7.47019e-12 3 6.825486121971558e-01 6.825486121958232e-01 1.33260e-12 3.84299e-11 ----------------------------------------------------------------------------------------------------- 27 Ga 1 -1.048618014357803e+00 -1.048618014356240e+00 1.56297e-12 1.57625e-11 2 -1.793300918057745e+00 -1.793300918054492e+00 3.25318e-12 8.90599e-12 3 -5.487322294329589e-01 -5.487322294383388e-01 5.37992e-12 5.35209e-11 ----------------------------------------------------------------------------------------------------- 28 Ga 1 6.280881983825934e-01 6.280881983849710e-01 2.37754e-12 2.37828e-11 2 -7.566585102742693e-02 -7.566585102823753e-02 8.10602e-13 1.11277e-11 3 -2.481682465844695e+00 -2.481682465844506e+00 1.88738e-13 1.42695e-11 ----------------------------------------------------------------------------------------------------- 29 Ga 1 1.110012189742879e+00 1.110012189745359e+00 2.47957e-12 7.36309e-11 2 1.741566388848208e-01 1.741566388813865e-01 3.43425e-12 2.19201e-11 3 9.026800075963737e-03 9.026800077065463e-03 1.10173e-12 3.99359e-11 ----------------------------------------------------------------------------------------------------- 30 Ga 1 -2.429979091804916e+00 -2.429979091804741e+00 1.74527e-13 1.23603e-11 2 -1.776098357046290e+00 -1.776098357049350e+00 3.06000e-12 7.27949e-11 3 -1.485092368244114e+00 -1.485092368247483e+00 3.36908e-12 1.00726e-11 ----------------------------------------------------------------------------------------------------- 31 Ga 1 -2.742280880794093e+00 -2.742280880792171e+00 1.92157e-12 2.03668e-11 2 -2.715999274484870e+00 -2.715999274485475e+00 6.05294e-13 2.26712e-11 3 1.375173130656691e-01 1.375173130681705e-01 2.50144e-12 5.12557e-12 ----------------------------------------------------------------------------------------------------- 32 Ga 1 1.021877323579381e+00 1.021877323584433e+00 5.05196e-12 2.39497e-12 2 6.657572399357834e-01 6.657572399328930e-01 2.89035e-12 1.14586e-11 3 3.839304871121028e-01 3.839304871180679e-01 5.96512e-12 2.39134e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 29, direction = 3: |F_model - F_numer| error = --------------------------------- = 1.22051e-10 max{(|F_model|+|F_numer|)/2, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = N | a0 = 3.06042385101 | (Configuration in file "config-N.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 2.229017231993950e+00 2.229017231994709e+00 7.59837e-13 1.00173e-11 2 1.676068406799537e+00 1.676068406799400e+00 1.37446e-13 3.66662e-12 3 3.392603824650408e+00 3.392603824651819e+00 1.41087e-12 1.41509e-11 ----------------------------------------------------------------------------------------------------- 2 N 1 -1.572449312886371e+00 -1.572449312882811e+00 3.55938e-12 1.58769e-11 2 5.523023936399388e-01 5.523023936396768e-01 2.62013e-13 1.42585e-09 * 3 -4.580706135413861e-01 -4.580706135402257e-01 1.16035e-12 6.49980e-12 ----------------------------------------------------------------------------------------------------- 3 N 1 3.548315956446323e-01 3.548315956404629e-01 4.16939e-12 8.40661e-13 2 -4.921597847658643e-01 -4.921597847650448e-01 8.19511e-13 6.77386e-12 3 -3.296630873322992e+00 -3.296630873322145e+00 8.46434e-13 5.62084e-12 ----------------------------------------------------------------------------------------------------- 4 N 1 -2.108237696421397e+00 -2.108237696420581e+00 8.16236e-13 6.93667e-12 2 1.710149633696772e+00 1.710149633700104e+00 3.33178e-12 5.86342e-11 3 -8.361402466804818e-01 -8.361402466871807e-01 6.69886e-12 4.01692e-11 ----------------------------------------------------------------------------------------------------- 5 N 1 -1.681554026824132e+00 -1.681554026824336e+00 2.04503e-13 5.84204e-11 2 -9.478658981990840e-01 -9.478658981997485e-01 6.64580e-13 1.56528e-11 3 3.132397511716976e+00 3.132397511718047e+00 1.07114e-12 4.44622e-12 ----------------------------------------------------------------------------------------------------- 6 N 1 -3.199151008675059e+00 -3.199151008677281e+00 2.22222e-12 1.25389e-11 2 4.702875244802819e-01 4.702875244847227e-01 4.44078e-12 1.38042e-10 * 3 3.133451364709495e+00 3.133451364709970e+00 4.75620e-13 7.80398e-12 ----------------------------------------------------------------------------------------------------- 7 N 1 -3.369963675785447e+00 -3.369963675791730e+00 6.28342e-12 1.34515e-12 2 3.637433041427264e+00 3.637433041422093e+00 5.17142e-12 7.36584e-11 3 -3.602018781277955e-01 -3.602018781313867e-01 3.59118e-12 1.18733e-11 ----------------------------------------------------------------------------------------------------- 8 N 1 6.910190996704093e+00 6.910190996697118e+00 6.97487e-12 3.10898e-11 2 -4.831622160721903e+00 -4.831622160720801e+00 1.10134e-12 1.36442e-11 3 -8.323908640680044e-01 -8.323908640639395e-01 4.06497e-12 1.39746e-11 ----------------------------------------------------------------------------------------------------- 9 N 1 1.228912015253315e+00 1.228912015251058e+00 2.25708e-12 5.53091e-12 2 -1.655043504633487e+00 -1.655043504628806e+00 4.68159e-12 4.70601e-12 3 5.422095930446102e-01 5.422095930468619e-01 2.25164e-12 7.16749e-12 ----------------------------------------------------------------------------------------------------- 10 N 1 6.060189520941252e-01 6.060189520934055e-01 7.19647e-13 1.77206e-11 2 -1.562957312028999e+00 -1.562957312029291e+00 2.91323e-13 7.16072e-12 3 2.631677428612475e+00 2.631677428611854e+00 6.20393e-13 8.30580e-12 ----------------------------------------------------------------------------------------------------- 11 N 1 -3.184326591295069e+00 -3.184326591299235e+00 4.16600e-12 1.83085e-11 2 1.415927190000232e+00 1.415927189992729e+00 7.50289e-12 2.67966e-11 3 -2.207726488332613e+00 -2.207726488332100e+00 5.13367e-13 5.33436e-11 ----------------------------------------------------------------------------------------------------- 12 N 1 2.227265776873057e+00 2.227265776873426e+00 3.68594e-13 4.11213e-11 2 -1.551163622516015e+00 -1.551163622516453e+00 4.37872e-13 7.24310e-12 3 3.172196547929967e+00 3.172196547926155e+00 3.81251e-12 2.69500e-11 ----------------------------------------------------------------------------------------------------- 13 N 1 3.450210558718054e+00 3.450210558725018e+00 6.96465e-12 8.06732e-12 2 -7.419173110554567e-01 -7.419173110545706e-01 8.86069e-13 2.69833e-11 3 -1.599452074733659e+00 -1.599452074734115e+00 4.56746e-13 3.00269e-11 ----------------------------------------------------------------------------------------------------- 14 N 1 -6.008825991286071e-01 -6.008825991266556e-01 1.95144e-12 2.34425e-11 2 -3.520139818801399e-02 -3.520139818934458e-02 1.33059e-12 5.12172e-12 3 -4.939425943903860e-01 -4.939425943898967e-01 4.89220e-13 4.74731e-13 ----------------------------------------------------------------------------------------------------- 15 N 1 1.144665967625629e+00 1.144665967625347e+00 2.82441e-13 6.03499e-11 2 -1.250193756023611e+00 -1.250193756019967e+00 3.64464e-12 1.04159e-11 3 2.452183924909842e-01 2.452183924795695e-01 1.14146e-11 3.97359e-11 ----------------------------------------------------------------------------------------------------- 16 N 1 -1.288959880485178e+00 -1.288959880485835e+00 6.56364e-13 7.37899e-12 2 2.542226431876998e+00 2.542226431867129e+00 9.86899e-12 7.45226e-12 3 -1.101077531348775e+00 -1.101077531349164e+00 3.88800e-13 1.83118e-11 ----------------------------------------------------------------------------------------------------- 17 N 1 3.169989913529603e+00 3.169989913532206e+00 2.60370e-12 4.90985e-12 2 1.479626805435635e+00 1.479626805431955e+00 3.67950e-12 8.46079e-12 3 -2.142498705381678e-02 -2.142498705559856e-02 1.78178e-12 2.04156e-11 ----------------------------------------------------------------------------------------------------- 18 N 1 -1.994551754001214e+00 -1.994551754006510e+00 5.29576e-12 2.25915e-11 2 -2.228475099885090e+00 -2.228475099896786e+00 1.16964e-11 5.12301e-12 3 1.156980977044995e+00 1.156980977045984e+00 9.89431e-13 9.04454e-12 ----------------------------------------------------------------------------------------------------- 19 N 1 -5.454238005109735e-01 -5.454238005144395e-01 3.46601e-12 4.33961e-11 2 2.757345173141983e+00 2.757345173137964e+00 4.01901e-12 3.59184e-11 3 -1.718533766281000e+00 -1.718533766280112e+00 8.87956e-13 1.02203e-11 ----------------------------------------------------------------------------------------------------- 20 N 1 2.011310823883063e+00 2.011310823886665e+00 3.60112e-12 6.52323e-12 2 -1.280339095547127e+00 -1.280339095545223e+00 1.90403e-12 4.59586e-11 3 -1.000897682112262e+00 -1.000897682113275e+00 1.01297e-12 1.37335e-12 ----------------------------------------------------------------------------------------------------- 21 N 1 6.991913435364633e-01 6.991913435395319e-01 3.06866e-12 1.16890e-11 2 1.795285833360219e+00 1.795285833360115e+00 1.03917e-13 4.46954e-12 3 1.363978113705664e+00 1.363978113706141e+00 4.76508e-13 1.09470e-11 ----------------------------------------------------------------------------------------------------- 22 N 1 -1.363578936733528e+00 -1.363578936733269e+00 2.59126e-13 2.22700e-11 2 2.106350682371907e+00 2.106350682369581e+00 2.32570e-12 3.66578e-11 3 5.865644843145421e-01 5.865644843143131e-01 2.29039e-13 1.86663e-11 ----------------------------------------------------------------------------------------------------- 23 N 1 -3.799545991950559e+00 -3.799545991950100e+00 4.58300e-13 1.71174e-11 2 2.085901214528992e+00 2.085901214528147e+00 8.45546e-13 4.90052e-12 3 -1.836541147261521e+00 -1.836541147261123e+00 3.98348e-13 3.41860e-12 ----------------------------------------------------------------------------------------------------- 24 N 1 1.619134298208784e+00 1.619134298210535e+00 1.75082e-12 7.90679e-11 2 -4.186371938056293e+00 -4.186371938056321e+00 2.75335e-14 2.11413e-11 3 1.029722725562759e-01 1.029722725494423e-01 6.83364e-12 7.64663e-12 ----------------------------------------------------------------------------------------------------- 25 N 1 3.444940940237606e-01 3.444940940253579e-01 1.59728e-12 8.11832e-11 2 -9.124416369144170e-01 -9.124416369125787e-01 1.83831e-12 1.15730e-11 3 -1.891979104895977e+00 -1.891979104891949e+00 4.02811e-12 1.41265e-11 ----------------------------------------------------------------------------------------------------- 26 N 1 -2.841087543677124e+00 -2.841087543678280e+00 1.15552e-12 3.54867e-11 2 3.653550515548900e-01 3.653550515647873e-01 9.89725e-12 3.83154e-11 3 1.117722603843376e+00 1.117722603851435e+00 8.05978e-12 5.55285e-11 ----------------------------------------------------------------------------------------------------- 27 N 1 -8.722198617861857e-01 -8.722198617833463e-01 2.83940e-12 8.01537e-12 2 3.704938119728182e+00 3.704938119730346e+00 2.16449e-12 2.13913e-11 3 -6.420954695550569e-01 -6.420954695536296e-01 1.42730e-12 8.22142e-12 ----------------------------------------------------------------------------------------------------- 28 N 1 4.006950214503815e+00 4.006950214505931e+00 2.11653e-12 2.86331e-11 2 -1.616126362195103e+00 -1.616126362193604e+00 1.49925e-12 1.57570e-11 3 -2.357777658963398e+00 -2.357777658962243e+00 1.15552e-12 7.41451e-12 ----------------------------------------------------------------------------------------------------- 29 N 1 1.654163873606224e-01 1.654163873617004e-01 1.07800e-12 1.22833e-11 2 4.456722053947766e-01 4.456722053926895e-01 2.08705e-12 7.54437e-11 3 1.711136091207639e+00 1.711136091206792e+00 8.46434e-13 1.79841e-11 ----------------------------------------------------------------------------------------------------- 30 N 1 -1.146414939510612e+00 -1.146414939511980e+00 1.36735e-12 1.09983e-11 2 -7.999706399201999e-01 -7.999706399272970e-01 7.09710e-12 1.22621e-11 3 2.371378351643079e+00 2.371378351643424e+00 3.45057e-13 2.24052e-11 ----------------------------------------------------------------------------------------------------- 31 N 1 2.313443789250414e-01 2.313443789255803e-01 5.38847e-13 8.08826e-11 2 1.788477276862395e-01 1.788477276903357e-01 4.09622e-12 7.42969e-11 3 -2.939963746970578e+00 -2.939963746967103e+00 3.47500e-12 9.84457e-12 ----------------------------------------------------------------------------------------------------- 32 N 1 -8.305969292065509e-01 -8.305969292133685e-01 6.81755e-12 6.09636e-11 2 -2.831867914473178e+00 -2.831867914469790e+00 3.38884e-12 1.40323e-11 3 -1.065640829830784e+00 -1.065640829833729e+00 2.94431e-12 2.27551e-12 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 17, direction = 3: |F_model - F_numer| error = --------------------------------- = 8.31635e-11 max{(|F_model|+|F_numer|)/2, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = Ga N | a0 = 3.48298280937 | (Configuration in file "config-GaN.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 1.136361979291762e+00 1.136361979292427e+00 6.65024e-13 1.25162e-11 2 -6.476808840144234e-02 -6.476808840264672e-02 1.20438e-12 3.79759e-11 3 -1.345180237751557e+00 -1.345180237748398e+00 3.15858e-12 1.89617e-11 ----------------------------------------------------------------------------------------------------- 2 Ga 1 -2.071449553000476e+00 -2.071449552990405e+00 1.00715e-11 4.36955e-10 * 2 -2.079533269177455e+00 -2.079533269190856e+00 1.34013e-11 6.00129e-11 3 -6.255144405840961e+00 -6.255144405840532e+00 4.28990e-13 1.53584e-10 ----------------------------------------------------------------------------------------------------- 3 N 1 -1.276951057378283e+01 -1.276951057379162e+01 8.79119e-12 4.78959e-11 2 -4.296688821656946e+00 -4.296688821659433e+00 2.48690e-12 6.41647e-11 3 -7.958220172494991e+00 -7.958220172499522e+00 4.53060e-12 8.71569e-12 ----------------------------------------------------------------------------------------------------- 4 Ga 1 -9.898165222905842e+00 -9.898165222911095e+00 5.25269e-12 7.07008e-11 2 1.515284490002953e+00 1.515284489994291e+00 8.66129e-12 6.84144e-11 3 -7.488730711736431e-01 -7.488730711817955e-01 8.15237e-12 2.88657e-11 ----------------------------------------------------------------------------------------------------- 5 Ga 1 2.501241543561192e+00 2.501241543563078e+00 1.88649e-12 8.11662e-12 2 -1.699731629434347e+00 -1.699731629434495e+00 1.47660e-13 3.04283e-11 3 -2.848813587586410e+00 -2.848813587587106e+00 6.95444e-13 5.43063e-11 ----------------------------------------------------------------------------------------------------- 6 N 1 -2.720318043398476e+00 -2.720318043400725e+00 2.24931e-12 2.60156e-11 2 -2.920473285701847e-01 -2.920473285707826e-01 5.97911e-13 3.03058e-12 3 5.789076525130046e-01 5.789076525115907e-01 1.41387e-12 2.27934e-11 ----------------------------------------------------------------------------------------------------- 7 N 1 1.600669788202101e+01 1.600669788202258e+01 1.57385e-12 2.18527e-11 2 -3.934667594712249e+00 -3.934667594713195e+00 9.45910e-13 3.93614e-11 3 -1.395703103020367e+01 -1.395703103019716e+01 6.50680e-12 6.72227e-11 ----------------------------------------------------------------------------------------------------- 8 Ga 1 3.992614680652156e+00 3.992614681380826e+00 7.28670e-10 2.53380e-09 * 2 1.100151534477799e+01 1.100151534550704e+01 7.29058e-10 2.39651e-09 * 3 -1.136759690989876e+01 -1.136759690989584e+01 2.91323e-12 2.97346e-10 * ----------------------------------------------------------------------------------------------------- 9 N 1 -2.851457382623139e-01 -2.851457382653795e-01 3.06560e-12 4.98817e-11 2 4.189787237341598e-01 4.189787237351897e-01 1.02990e-12 2.96251e-11 3 4.409903914756731e-01 4.409903915003114e-01 2.46383e-11 6.85098e-11 ----------------------------------------------------------------------------------------------------- 10 N 1 4.688077181963989e-01 4.688077181954274e-01 9.71556e-13 6.91897e-12 2 -3.507937154056870e-01 -3.507937154066948e-01 1.00780e-12 3.20079e-11 3 1.716975213420483e+00 1.716975213418518e+00 1.96576e-12 1.67351e-11 ----------------------------------------------------------------------------------------------------- 11 Ga 1 2.170189861137461e+00 2.170189861592626e+00 4.55166e-10 1.93099e-09 * 2 4.330066706252675e+00 4.330066706401356e+00 1.48681e-10 1.32520e-09 * 3 1.505789207340529e+00 1.505789207327932e+00 1.25966e-11 1.03959e-09 * ----------------------------------------------------------------------------------------------------- 12 Ga 1 2.875853634287739e-01 2.875853634265145e-01 2.25947e-12 4.92007e-11 2 7.059492378183282e-01 7.059492378199071e-01 1.57896e-12 1.69423e-11 3 -1.886710350505907e+00 -1.886710350514666e+00 8.75833e-12 9.77107e-12 ----------------------------------------------------------------------------------------------------- 13 Ga 1 4.128036644870342e+00 4.128036644871007e+00 6.65246e-13 7.66942e-12 2 1.511033893233858e+00 1.511033893230389e+00 3.46967e-12 8.70148e-12 3 -5.505520688864652e+00 -5.505520688864059e+00 5.93303e-13 1.24717e-10 ----------------------------------------------------------------------------------------------------- 14 N 1 -1.538936003720725e+00 -1.538936003723043e+00 2.31837e-12 1.75620e-11 2 -6.629161976466224e-01 -6.629161976457335e-01 8.88845e-13 1.03496e-10 3 8.983333682941419e-01 8.983333683015381e-01 7.39619e-12 2.29269e-11 ----------------------------------------------------------------------------------------------------- 15 N 1 1.928669898662186e+01 1.928669898662978e+01 7.92255e-12 6.63967e-11 2 -8.002458421417026e+00 -8.002458421388489e+00 2.85372e-11 6.46079e-11 3 -2.243266005219427e+01 -2.243266005222511e+01 3.08376e-11 7.15765e-11 ----------------------------------------------------------------------------------------------------- 16 Ga 1 1.927308897697075e+00 1.927308897686050e+00 1.10243e-11 6.00475e-11 2 5.325932319448126e+00 5.325932319446633e+00 1.49303e-12 1.42704e-11 3 -1.709736894539157e+00 -1.709736894539680e+00 5.23581e-13 2.95879e-11 ----------------------------------------------------------------------------------------------------- 17 Ga 1 -5.089270469347236e+00 -5.089270469365489e+00 1.82530e-11 2.13900e-11 2 -4.499824235067155e+00 -4.499824235063041e+00 4.11404e-12 8.30527e-11 3 2.346235194233281e+00 2.346235194235623e+00 2.34213e-12 1.05955e-11 ----------------------------------------------------------------------------------------------------- 18 N 1 -1.582115021295056e+01 -1.582115021294356e+01 6.99885e-12 3.63745e-11 2 1.045158121894116e+01 1.045158121894916e+01 7.99893e-12 1.33689e-11 3 -3.699895295764300e+00 -3.699895295772703e+00 8.40306e-12 4.31832e-11 ----------------------------------------------------------------------------------------------------- 19 Ga 1 -1.109388939731676e+00 -1.109388939731202e+00 4.74065e-13 1.08566e-11 2 -2.268622276740592e+00 -2.268622276738095e+00 2.49667e-12 1.60902e-11 3 1.183056815357119e+00 1.183056815357269e+00 1.50102e-13 9.69891e-12 ----------------------------------------------------------------------------------------------------- 20 Ga 1 -1.543561787255649e+00 -1.543561787256245e+00 5.95524e-13 1.75371e-12 2 -2.031869729168023e+00 -2.031869729167818e+00 2.04725e-13 3.55977e-11 3 2.977784327251806e+00 2.977784327253267e+00 1.46105e-12 1.84563e-11 ----------------------------------------------------------------------------------------------------- 21 N 1 1.056111645554802e+01 1.056111645553928e+01 8.74678e-12 2.74271e-10 * 2 -2.467777905035266e+01 -2.467777905034707e+01 5.59197e-12 2.94094e-11 3 3.268145205742086e+01 3.268145205742601e+01 5.14433e-12 9.88010e-11 ----------------------------------------------------------------------------------------------------- 22 Ga 1 1.020542593868226e+01 1.020542593868418e+01 1.91491e-12 7.28839e-12 2 1.495904709644118e+00 1.495904709639260e+00 4.85723e-12 6.77922e-11 3 5.052732009947984e+00 5.052732009946954e+00 1.02940e-12 5.13172e-11 ----------------------------------------------------------------------------------------------------- 23 N 1 -1.652946597148380e-01 -1.652946597156403e-01 8.02275e-13 3.32601e-11 2 1.238350493667145e+00 1.238350493673196e+00 6.05049e-12 3.03451e-11 3 -8.468083306013144e-01 -8.468083306003497e-01 9.64784e-13 4.10605e-12 ----------------------------------------------------------------------------------------------------- 24 Ga 1 2.901403141027072e+00 2.901403141035864e+00 8.79252e-12 1.24118e-11 2 3.121217452534992e+00 3.121217452537248e+00 2.25597e-12 4.88409e-11 3 4.599300727446951e+00 4.599300727442265e+00 4.68603e-12 1.86073e-12 ----------------------------------------------------------------------------------------------------- 25 Ga 1 -4.049932553574611e+00 -4.049932553603608e+00 2.89972e-11 1.74472e-10 2 1.973738298532637e+00 1.973738298527206e+00 5.43188e-12 3.61336e-10 * 3 -2.071183918993971e+00 -2.071183919000447e+00 6.47660e-12 2.36621e-10 * ----------------------------------------------------------------------------------------------------- 26 N 1 -2.887500886124452e+01 -2.887500886127295e+01 2.84253e-11 5.91385e-11 2 1.692078416301062e+01 1.692078416301534e+01 4.72156e-12 1.87157e-11 3 -1.209214102676447e+01 -1.209214102676310e+01 1.36602e-12 8.22862e-11 ----------------------------------------------------------------------------------------------------- 27 Ga 1 4.362994274654988e+00 4.362994274658102e+00 3.11395e-12 3.71347e-12 2 1.703157272914333e+00 1.703157272914009e+00 3.23519e-13 4.32023e-11 3 7.457109493776631e+00 7.457109493770508e+00 6.12310e-12 1.27205e-11 ----------------------------------------------------------------------------------------------------- 28 Ga 1 -8.356847373599273e-01 -8.356847373634814e-01 3.55405e-12 1.29693e-11 2 2.158284806934073e+00 2.158284806935350e+00 1.27676e-12 3.38130e-12 3 1.207275292956975e+00 1.207275292955160e+00 1.81499e-12 9.47531e-12 ----------------------------------------------------------------------------------------------------- 29 N 1 -9.138347196173550e+00 -9.138347196172516e+00 1.03384e-12 1.21707e-10 2 -1.970412952957204e+01 -1.970412952956994e+01 2.09965e-12 4.86544e-11 3 1.572366035529574e+01 1.572366035528738e+01 8.36486e-12 8.63452e-11 ----------------------------------------------------------------------------------------------------- 30 N 1 5.383278474788018e+00 5.383278474793291e+00 5.27223e-12 5.09726e-11 2 1.123066972915257e+01 1.123066972912440e+01 2.81730e-11 1.57469e-10 3 5.401913584126315e+00 5.401913584131746e+00 5.43121e-12 1.21441e-11 ----------------------------------------------------------------------------------------------------- 31 N 1 -9.659267789870883e-01 -9.659267789885435e-01 1.45517e-12 2.57779e-11 2 -1.406919121071206e+00 -1.406919121072649e+00 1.44329e-12 2.07518e-11 3 -4.641478748249760e-01 -4.641478748215232e-01 3.45285e-12 2.66076e-12 ----------------------------------------------------------------------------------------------------- 32 N 1 1.155732948923193e+01 1.155732948922429e+01 7.63301e-12 6.90843e-11 2 8.703001477938326e-01 8.703001477913391e-01 2.49345e-12 5.60407e-12 3 1.141814815714552e+01 1.141814815715375e+01 8.22631e-12 8.70966e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 9, direction = 3: |F_model - F_numer| error = --------------------------------- = 5.58704e-11 max{(|F_model|+|F_numer|)/2, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.22051e-10 Machine precision = 2.22045e-16 Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 1.22051e-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. 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.