!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_NordAlbeErhart_2003_GaN__MO_612061685362_003 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 = 3.9710893630981445 | (Configuration in file "config-Ga.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ga 1 6.089485951165599e+00 6.089485951163527e+00 2.07212e-12 3.76374e-11 2 2.691953275397380e+00 2.691953275401763e+00 4.38360e-12 1.84746e-11 3 2.510907937519865e+00 2.510907937517199e+00 2.66631e-12 2.36970e-11 ----------------------------------------------------------------------------------------------------- 2 Ga 1 -2.569437033826246e+00 -2.569437033842031e+00 1.57847e-11 4.03406e-11 2 -1.498537171250781e+00 -1.498537171258274e+00 7.49334e-12 9.31124e-11 3 3.221179908937704e+00 3.221179908938344e+00 6.40821e-13 2.78533e-11 ----------------------------------------------------------------------------------------------------- 3 Ga 1 -2.025555993868591e+00 -2.025555993870975e+00 2.38387e-12 5.25135e-12 2 2.728750936193485e+00 2.728750936196276e+00 2.79110e-12 8.04752e-11 3 -5.025870094179252e+00 -5.025870094181365e+00 2.11298e-12 2.37099e-11 ----------------------------------------------------------------------------------------------------- 4 Ga 1 3.874855880907573e+00 3.874855880910364e+00 2.79066e-12 1.58500e-11 2 6.956503143758007e-01 6.956503143848872e-01 9.08651e-12 1.14940e-11 3 1.104124705111786e+00 1.104124705109009e+00 2.77667e-12 2.33575e-11 ----------------------------------------------------------------------------------------------------- 5 Ga 1 3.937306088788208e-01 3.937306088795302e-01 7.09321e-13 1.18201e-10 2 2.349765825286505e+00 2.349765825284865e+00 1.64047e-12 4.35514e-11 3 3.564516535253299e+00 3.564516535253009e+00 2.89546e-13 3.91838e-11 ----------------------------------------------------------------------------------------------------- 6 Ga 1 -3.293247047549600e+00 -3.293247047553327e+00 3.72680e-12 3.54889e-11 2 -1.002293161314598e+00 -1.002293161311538e+00 3.06022e-12 6.31972e-11 3 1.466878728997633e+00 1.466878728997765e+00 1.32117e-13 8.96350e-11 ----------------------------------------------------------------------------------------------------- 7 Ga 1 -7.681997212229635e-01 -7.681997212220082e-01 9.55347e-13 5.00080e-11 2 -7.011845005041359e-01 -7.011845005038407e-01 2.95208e-13 3.16461e-11 3 -2.566297805541105e+00 -2.566297805542177e+00 1.07248e-12 3.11657e-11 ----------------------------------------------------------------------------------------------------- 8 Ga 1 -1.267251589120630e+00 -1.267251589121176e+00 5.46008e-13 4.85127e-11 2 -1.592428312632245e+00 -1.592428312632919e+00 6.73905e-13 4.19471e-11 3 -5.976337332814237e-01 -5.976337332836320e-01 2.20834e-12 5.31661e-11 ----------------------------------------------------------------------------------------------------- 9 Ga 1 -2.749303193545896e-01 -2.749303193525488e-01 2.04081e-12 6.45204e-11 2 -1.786512596637748e+00 -1.786512596634768e+00 2.97984e-12 2.87588e-11 3 2.000713265438873e+00 2.000713265443453e+00 4.57989e-12 4.78331e-10 * ----------------------------------------------------------------------------------------------------- 10 Ga 1 -1.637199452346389e+00 -1.637199452347657e+00 1.26765e-12 7.96476e-11 2 -5.756025725900715e-01 -5.756025725927528e-01 2.68130e-12 6.20272e-11 3 2.073838104652293e+00 2.073838104650228e+00 2.06501e-12 7.07265e-11 ----------------------------------------------------------------------------------------------------- 11 Ga 1 -1.264702641297836e+00 -1.264702641300668e+00 2.83262e-12 1.04095e-10 2 -2.185087836852633e+00 -2.185087836855966e+00 3.33245e-12 3.79838e-11 3 -1.193521107580749e+00 -1.193521107584988e+00 4.23839e-12 4.07685e-11 ----------------------------------------------------------------------------------------------------- 12 Ga 1 2.857736513083125e+00 2.857736513081800e+00 1.32472e-12 5.26610e-11 2 -8.933501549354483e-01 -8.933501549383884e-01 2.94009e-12 1.53971e-10 3 -2.155068251451934e+00 -2.155068251447535e+00 4.39915e-12 2.73603e-12 ----------------------------------------------------------------------------------------------------- 13 Ga 1 -1.054032651279646e+00 -1.054032651281572e+00 1.92579e-12 5.99909e-11 2 2.118207367556407e-01 2.118207367495551e-01 6.08555e-12 1.62768e-10 3 -2.386148421989059e+00 -2.386148421991782e+00 2.72316e-12 2.14824e-11 ----------------------------------------------------------------------------------------------------- 14 Ga 1 -9.861808454799790e-01 -9.861808454796448e-01 3.34177e-13 1.17586e-11 2 -3.275254270671228e-01 -3.275254270679883e-01 8.65530e-13 4.02078e-12 3 9.034719129587313e-01 9.034719129648259e-01 6.09457e-12 1.37692e-11 ----------------------------------------------------------------------------------------------------- 15 Ga 1 2.352681575509355e+00 2.352681575501210e+00 8.14504e-12 1.49489e-11 2 4.824681461122549e-01 4.824681461166749e-01 4.42002e-12 6.00408e-11 3 2.621151176823464e+00 2.621151176820398e+00 3.06599e-12 2.90235e-11 ----------------------------------------------------------------------------------------------------- 16 Ga 1 2.308569029269391e+00 2.308569029275912e+00 6.52145e-12 2.21698e-11 2 5.997487533244049e-01 5.997487533270802e-01 2.67530e-12 2.01190e-11 3 1.213988889249468e-01 1.213988889233466e-01 1.60021e-12 9.63272e-11 ----------------------------------------------------------------------------------------------------- 17 Ga 1 1.241981811208290e+00 1.241981811210199e+00 1.90892e-12 1.07343e-11 2 2.046125626799446e+00 2.046125626798023e+00 1.42331e-12 1.86868e-11 3 -1.810732341989230e+00 -1.810732341991757e+00 2.52620e-12 3.31029e-11 ----------------------------------------------------------------------------------------------------- 18 Ga 1 -1.789855045301904e+00 -1.789855045308807e+00 6.90292e-12 8.59357e-12 2 -9.091478230184610e-01 -9.091478230181971e-01 2.63900e-13 2.88881e-11 3 2.092418287842413e+00 2.092418287842387e+00 2.66454e-14 2.80926e-11 ----------------------------------------------------------------------------------------------------- 19 Ga 1 3.061557646183132e+00 3.061557646177285e+00 5.84732e-12 4.76390e-10 * 2 1.323783406172840e+00 1.323783406169060e+00 3.77987e-12 1.23230e-11 3 -1.773828836742637e+00 -1.773828836742495e+00 1.42553e-13 4.10161e-12 ----------------------------------------------------------------------------------------------------- 20 Ga 1 2.118274507856515e+00 2.118274507851994e+00 4.52083e-12 3.68163e-11 2 1.005673711840505e-01 1.005673711836005e-01 4.50043e-13 5.42781e-12 3 -2.129880401201761e+00 -2.129880401203974e+00 2.21378e-12 1.68083e-11 ----------------------------------------------------------------------------------------------------- 21 Ga 1 -3.925343763204227e+00 -3.925343763203959e+00 2.67786e-13 3.17861e-11 2 4.217455439531151e+00 4.217455439528654e+00 2.49756e-12 6.11067e-11 3 5.158725354356695e+00 5.158725354355876e+00 8.18901e-13 5.22897e-11 ----------------------------------------------------------------------------------------------------- 22 Ga 1 -7.411484307880055e-01 -7.411484307823066e-01 5.69889e-12 4.62478e-11 2 1.689117519512635e+00 1.689117519516668e+00 4.03255e-12 2.12774e-11 3 -3.891953502799481e-01 -3.891953502706968e-01 9.25121e-12 7.91337e-11 ----------------------------------------------------------------------------------------------------- 23 Ga 1 -3.300861143557905e+00 -3.300861143558595e+00 6.90115e-13 5.65459e-12 2 2.202171525060445e+00 2.202171525060090e+00 3.54827e-13 1.00897e-11 3 -8.906648892247530e-01 -8.906648892282838e-01 3.53084e-12 9.29012e-12 ----------------------------------------------------------------------------------------------------- 24 Ga 1 3.502135222910076e+00 3.502135222909351e+00 7.24754e-13 1.71134e-11 2 -2.605986567072111e+00 -2.605986567073105e+00 9.94316e-13 4.44400e-12 3 -4.337842428503486e+00 -4.337842428506611e+00 3.12461e-12 1.20773e-10 ----------------------------------------------------------------------------------------------------- 25 Ga 1 2.227317753156537e+00 2.227317753146981e+00 9.55591e-12 3.43561e-11 2 -2.009053149866856e+00 -2.009053149868846e+00 1.99085e-12 7.43006e-12 3 1.719842706218578e+00 1.719842706213550e+00 5.02842e-12 2.18454e-11 ----------------------------------------------------------------------------------------------------- 26 Ga 1 -1.669480546677910e+00 -1.669480546675738e+00 2.17248e-12 9.66298e-11 2 2.684809198319522e-01 2.684809198314083e-01 5.43954e-13 3.24751e-12 3 6.825486121971519e-01 6.825486122016726e-01 4.52072e-12 2.16082e-11 ----------------------------------------------------------------------------------------------------- 27 Ga 1 -1.048618014357744e+00 -1.048618014354191e+00 3.55271e-12 1.73546e-11 2 -1.793300918057738e+00 -1.793300918055178e+00 2.56040e-12 8.31557e-12 3 -5.487322294328751e-01 -5.487322294352669e-01 2.39175e-12 2.52999e-11 ----------------------------------------------------------------------------------------------------- 28 Ga 1 6.280881983825830e-01 6.280881983782021e-01 4.38094e-12 1.11529e-11 2 -7.566585102744999e-02 -7.566585102904701e-02 1.59701e-12 4.59160e-12 3 -2.481682465844736e+00 -2.481682465845250e+00 5.13811e-13 3.05658e-11 ----------------------------------------------------------------------------------------------------- 29 Ga 1 1.110012189742885e+00 1.110012189740900e+00 1.98508e-12 2.10110e-11 2 1.741566388848462e-01 1.741566388841065e-01 7.39686e-13 9.07551e-11 3 9.026800075952246e-03 9.026800072776286e-03 3.17596e-12 5.14478e-11 ----------------------------------------------------------------------------------------------------- 30 Ga 1 -2.429979091804984e+00 -2.429979091805319e+00 3.35731e-13 7.76623e-12 2 -1.776098357046361e+00 -1.776098357048097e+00 1.73617e-12 6.68108e-11 3 -1.485092368244212e+00 -1.485092368245851e+00 1.63936e-12 3.42182e-11 ----------------------------------------------------------------------------------------------------- 31 Ga 1 -2.742280880794121e+00 -2.742280880786177e+00 7.94342e-12 3.72014e-11 2 -2.715999274484886e+00 -2.715999274482479e+00 2.40741e-12 2.87872e-11 3 1.375173130656759e-01 1.375173130676947e-01 2.01886e-12 7.25262e-12 ----------------------------------------------------------------------------------------------------- 32 Ga 1 1.021877323579394e+00 1.021877323579502e+00 1.07692e-13 4.12204e-12 2 6.657572399357885e-01 6.657572399352523e-01 5.36238e-13 5.12590e-12 3 3.839304871121105e-01 3.839304871114694e-01 6.41098e-13 6.49641e-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 discontinuities. Maximum error obtained for particle = 29, direction = 3: |F_model - F_numer| error = ----------------------- = 3.51837e-10 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = N | a0 = 3.0604238510131836 | (Configuration in file "config-N.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 2.229017231993965e+00 2.229017231993387e+00 5.78204e-13 1.20570e-12 2 1.676068406799527e+00 1.676068406801331e+00 1.80411e-12 3.13771e-12 3 3.392603824650414e+00 3.392603824651450e+00 1.03562e-12 1.31442e-11 ----------------------------------------------------------------------------------------------------- 2 N 1 -1.572449312886381e+00 -1.572449312886830e+00 4.48752e-13 7.78555e-12 2 5.523023936399424e-01 5.523023936366451e-01 3.29725e-12 3.88645e-12 3 -4.580706135413844e-01 -4.580706135429265e-01 1.54210e-12 1.56943e-11 ----------------------------------------------------------------------------------------------------- 3 N 1 3.548315956446321e-01 3.548315956456879e-01 1.05582e-12 8.77964e-12 2 -4.921597847658496e-01 -4.921597847630845e-01 2.76512e-12 3.17908e-11 3 -3.296630873322994e+00 -3.296630873319763e+00 3.23164e-12 1.06919e-11 ----------------------------------------------------------------------------------------------------- 4 N 1 -2.108237696421435e+00 -2.108237696422095e+00 6.60361e-13 6.17311e-11 2 1.710149633696747e+00 1.710149633692216e+00 4.53038e-12 1.39571e-11 3 -8.361402466805178e-01 -8.361402466830815e-01 2.56373e-12 4.33996e-11 ----------------------------------------------------------------------------------------------------- 5 N 1 -1.681554026824143e+00 -1.681554026824814e+00 6.71463e-13 3.06977e-12 2 -9.478658981991062e-01 -9.478658981997612e-01 6.55032e-13 1.02345e-11 3 3.132397511716968e+00 3.132397511719571e+00 2.60370e-12 8.76543e-12 ----------------------------------------------------------------------------------------------------- 6 N 1 -3.199151008675044e+00 -3.199151008675236e+00 1.91402e-13 1.95555e-11 2 4.702875244802402e-01 4.702875244807006e-01 4.60354e-13 7.74558e-12 3 3.133451364709507e+00 3.133451364709634e+00 1.26565e-13 9.56568e-12 ----------------------------------------------------------------------------------------------------- 7 N 1 -3.369963675785457e+00 -3.369963675786654e+00 1.19682e-12 1.39218e-11 2 3.637433041427253e+00 3.637433041428542e+00 1.28875e-12 3.62177e-11 3 -3.602018781277854e-01 -3.602018781269690e-01 8.16403e-13 9.46349e-12 ----------------------------------------------------------------------------------------------------- 8 N 1 6.910190996704113e+00 6.910190996705308e+00 1.19460e-12 7.50138e-11 2 -4.831622160721856e+00 -4.831622160726440e+00 4.58389e-12 4.80966e-11 3 -8.323908640679883e-01 -8.323908640671842e-01 8.04135e-13 1.11525e-10 ----------------------------------------------------------------------------------------------------- 9 N 1 1.228912015253321e+00 1.228912015254648e+00 1.32760e-12 1.75249e-11 2 -1.655043504633467e+00 -1.655043504631110e+00 2.35723e-12 7.34923e-12 3 5.422095930446078e-01 5.422095930449892e-01 3.81362e-13 7.57971e-12 ----------------------------------------------------------------------------------------------------- 10 N 1 6.060189520941317e-01 6.060189520927614e-01 1.37035e-12 6.35436e-12 2 -1.562957312028991e+00 -1.562957312029038e+00 4.66294e-14 4.96914e-12 3 2.631677428612464e+00 2.631677428613151e+00 6.87006e-13 6.27809e-12 ----------------------------------------------------------------------------------------------------- 11 N 1 -3.184326591295067e+00 -3.184326591292530e+00 2.53753e-12 9.88454e-12 2 1.415927190000242e+00 1.415927189999880e+00 3.62599e-13 1.68690e-11 3 -2.207726488332600e+00 -2.207726488330457e+00 2.14273e-12 9.46798e-12 ----------------------------------------------------------------------------------------------------- 12 N 1 2.227265776873083e+00 2.227265776868591e+00 4.49196e-12 2.39462e-11 2 -1.551163622515998e+00 -1.551163622516188e+00 1.90070e-13 4.34786e-12 3 3.172196547929959e+00 3.172196547930992e+00 1.03295e-12 2.47282e-11 ----------------------------------------------------------------------------------------------------- 13 N 1 3.450210558718039e+00 3.450210558724379e+00 6.34026e-12 2.99814e-11 2 -7.419173110554119e-01 -7.419173110574044e-01 1.99252e-12 8.38196e-12 3 -1.599452074733638e+00 -1.599452074734688e+00 1.05027e-12 1.90249e-10 * ----------------------------------------------------------------------------------------------------- 14 N 1 -6.008825991286131e-01 -6.008825991276505e-01 9.62563e-13 3.82819e-11 2 -3.520139818802436e-02 -3.520139818784975e-02 1.74610e-13 1.07536e-12 3 -4.939425943903832e-01 -4.939425943900372e-01 3.46001e-13 2.46375e-12 ----------------------------------------------------------------------------------------------------- 15 N 1 1.144665967625631e+00 1.144665967622544e+00 3.08620e-12 8.54872e-12 2 -1.250193756023604e+00 -1.250193756019490e+00 4.11404e-12 8.18787e-11 3 2.452183924909368e-01 2.452183924926748e-01 1.73800e-12 1.11461e-11 ----------------------------------------------------------------------------------------------------- 16 N 1 -1.288959880485184e+00 -1.288959880483477e+00 1.70752e-12 1.62022e-11 2 2.542226431876976e+00 2.542226431873926e+00 3.05000e-12 1.59708e-11 3 -1.101077531348745e+00 -1.101077531343726e+00 5.01865e-12 2.17724e-11 ----------------------------------------------------------------------------------------------------- 17 N 1 3.169989913529601e+00 3.169989913528963e+00 6.38156e-13 1.98406e-11 2 1.479626805435628e+00 1.479626805435239e+00 3.89022e-13 2.28682e-11 3 -2.142498705382576e-02 -2.142498705809281e-02 4.26706e-12 5.92958e-11 ----------------------------------------------------------------------------------------------------- 18 N 1 -1.994551754001229e+00 -1.994551754011900e+00 1.06717e-11 2.88194e-11 2 -2.228475099885045e+00 -2.228475099883950e+00 1.09468e-12 2.80918e-11 3 1.156980977045035e+00 1.156980977046113e+00 1.07714e-12 7.58984e-11 ----------------------------------------------------------------------------------------------------- 19 N 1 -5.454238005110048e-01 -5.454238005076898e-01 3.31501e-12 5.88241e-11 2 2.757345173141988e+00 2.757345173151898e+00 9.90941e-12 4.29217e-11 3 -1.718533766280997e+00 -1.718533766276472e+00 4.52505e-12 4.26508e-11 ----------------------------------------------------------------------------------------------------- 20 N 1 2.011310823883059e+00 2.011310823883540e+00 4.81393e-13 3.19873e-11 2 -1.280339095547168e+00 -1.280339095547014e+00 1.53433e-13 1.07507e-11 3 -1.000897682112259e+00 -1.000897682115266e+00 3.00671e-12 2.25069e-11 ----------------------------------------------------------------------------------------------------- 21 N 1 6.991913435365302e-01 6.991913435356513e-01 8.78964e-13 5.40566e-11 2 1.795285833360196e+00 1.795285833358305e+00 1.89115e-12 2.65723e-11 3 1.363978113705661e+00 1.363978113705125e+00 5.35127e-13 1.07778e-11 ----------------------------------------------------------------------------------------------------- 22 N 1 -1.363578936733544e+00 -1.363578936732369e+00 1.17417e-12 5.29172e-11 2 2.106350682371910e+00 2.106350682375530e+00 3.62022e-12 3.48255e-11 3 5.865644843145479e-01 5.865644843143724e-01 1.75526e-13 4.25315e-12 ----------------------------------------------------------------------------------------------------- 23 N 1 -3.799545991950590e+00 -3.799545991949302e+00 1.28830e-12 1.33471e-11 2 2.085901214529002e+00 2.085901214528982e+00 1.99840e-14 7.10276e-12 3 -1.836541147261561e+00 -1.836541147261381e+00 1.80300e-13 2.02480e-11 ----------------------------------------------------------------------------------------------------- 24 N 1 1.619134298208803e+00 1.619134298211767e+00 2.96385e-12 9.26252e-11 2 -4.186371938056291e+00 -4.186371938057277e+00 9.86766e-13 3.95302e-11 3 1.029722725562884e-01 1.029722725584531e-01 2.16475e-12 9.84542e-11 ----------------------------------------------------------------------------------------------------- 25 N 1 3.444940940237883e-01 3.444940940217549e-01 2.03337e-12 2.95804e-11 2 -9.124416369144561e-01 -9.124416369119351e-01 2.52098e-12 9.76452e-12 3 -1.891979104895945e+00 -1.891979104897381e+00 1.43530e-12 4.33185e-11 ----------------------------------------------------------------------------------------------------- 26 N 1 -2.841087543677121e+00 -2.841087543677480e+00 3.59712e-13 7.95133e-11 2 3.653550515548775e-01 3.653550515561732e-01 1.29574e-12 2.04300e-11 3 1.117722603843336e+00 1.117722603842247e+00 1.08935e-12 1.17244e-11 ----------------------------------------------------------------------------------------------------- 27 N 1 -8.722198617861476e-01 -8.722198617887328e-01 2.58515e-12 1.07291e-11 2 3.704938119728200e+00 3.704938119726731e+00 1.46949e-12 3.39808e-11 3 -6.420954695550579e-01 -6.420954695562028e-01 1.14486e-12 4.87677e-12 ----------------------------------------------------------------------------------------------------- 28 N 1 4.006950214503809e+00 4.006950214502928e+00 8.81073e-13 3.07390e-11 2 -1.616126362195088e+00 -1.616126362191425e+00 3.66307e-12 1.23972e-11 3 -2.357777658963388e+00 -2.357777658969014e+00 5.62617e-12 3.98503e-11 ----------------------------------------------------------------------------------------------------- 29 N 1 1.654163873605881e-01 1.654163873600324e-01 5.55667e-13 4.27796e-11 2 4.456722053947461e-01 4.456722053957849e-01 1.03884e-12 9.39659e-12 3 1.711136091207596e+00 1.711136091204493e+00 3.10241e-12 5.19620e-11 ----------------------------------------------------------------------------------------------------- 30 N 1 -1.146414939510601e+00 -1.146414939512580e+00 1.97864e-12 2.80074e-11 2 -7.999706399201908e-01 -7.999706399179102e-01 2.28062e-12 2.84526e-11 3 2.371378351643068e+00 2.371378351651598e+00 8.52962e-12 7.76610e-11 ----------------------------------------------------------------------------------------------------- 31 N 1 2.313443789250394e-01 2.313443789266072e-01 1.56777e-12 9.30109e-11 2 1.788477276862484e-01 1.788477276820840e-01 4.16445e-12 1.59942e-11 3 -2.939963746970566e+00 -2.939963746964406e+00 6.16041e-12 4.26579e-11 ----------------------------------------------------------------------------------------------------- 32 N 1 -8.305969292065721e-01 -8.305969292078601e-01 1.28797e-12 1.64966e-10 * 2 -2.831867914473172e+00 -2.831867914474410e+00 1.23856e-12 2.18052e-11 3 -1.065640829830756e+00 -1.065640829831283e+00 5.27356e-13 1.61999e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 17, direction = 3: |F_model - F_numer| error = ----------------------- = 1.99163e-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 = Ga N | a0 = 3.722154952544952 | (Configuration in file "config-GaN.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 9.702877969937540e-01 9.702877969940967e-01 3.42726e-13 8.71858e-13 2 1.336133179495352e+00 1.336133179494898e+00 4.53415e-13 1.77809e-11 3 -3.530469525592479e-01 -3.530469525597755e-01 5.27633e-13 4.38621e-12 ----------------------------------------------------------------------------------------------------- 2 N 1 -1.499776796628493e+00 -1.499776796627523e+00 9.69225e-13 2.21632e-11 2 -1.778452560451200e+00 -1.778452560451217e+00 1.70974e-14 7.39953e-11 3 -4.050547523101215e-02 -4.050547523313159e-02 2.11944e-12 1.41425e-11 ----------------------------------------------------------------------------------------------------- 3 N 1 -7.031777562241026e+00 -7.031777562240369e+00 6.57252e-13 8.72458e-11 2 -5.976657949319230e+00 -5.976657949316747e+00 2.48246e-12 1.23511e-10 3 2.464725363123677e+00 2.464725363127687e+00 4.01013e-12 2.49631e-11 ----------------------------------------------------------------------------------------------------- 4 Ga 1 -1.928347480553567e+00 -1.928347480549320e+00 4.24705e-12 6.07041e-11 2 -1.732371378341726e+00 -1.732371378343499e+00 1.77325e-12 6.23990e-12 3 8.854413461719519e-01 8.854413461746637e-01 2.71183e-12 2.71493e-11 ----------------------------------------------------------------------------------------------------- 5 N 1 2.245634147194882e+00 2.245634147195304e+00 4.22329e-13 1.38729e-11 2 -1.201501678531007e+01 -1.201501678530290e+01 7.16582e-12 1.66612e-10 3 -1.337398134684897e+01 -1.337398134682106e+01 2.79101e-11 1.31893e-10 ----------------------------------------------------------------------------------------------------- 6 Ga 1 1.922237716658862e-01 1.922237716724147e-01 6.52856e-12 1.68257e-11 2 -2.344920533308638e+00 -2.344920533310282e+00 1.64357e-12 2.01328e-11 3 2.176907569104704e+00 2.176907569104000e+00 7.03881e-13 1.02739e-10 ----------------------------------------------------------------------------------------------------- 7 Ga 1 4.485940344983474e-01 4.485940344977003e-01 6.47149e-13 4.39691e-11 2 1.990609682435883e+00 1.990609682434789e+00 1.09424e-12 6.43059e-11 3 1.127202210380217e+00 1.127202210373796e+00 6.42131e-12 1.06284e-11 ----------------------------------------------------------------------------------------------------- 8 N 1 4.175762403893491e+00 4.175762403897767e+00 4.27569e-12 6.62466e-11 2 1.899800974968928e+01 1.899800974969212e+01 2.83862e-12 2.40252e-10 * 3 1.213432381315724e+01 1.213432381315451e+01 2.72316e-12 1.02171e-10 ----------------------------------------------------------------------------------------------------- 9 Ga 1 -1.566664287274916e+00 -1.566664287273834e+00 1.08225e-12 2.15781e-11 2 1.398982810460669e+00 1.398982810456072e+00 4.59632e-12 4.31610e-12 3 -2.075760821005730e+00 -2.075760821006246e+00 5.16476e-13 3.07221e-12 ----------------------------------------------------------------------------------------------------- 10 N 1 3.063103162082931e-01 3.063103162124904e-01 4.19731e-12 6.26277e-12 2 -2.259132108193293e+00 -2.259132108189114e+00 4.17888e-12 2.35909e-11 3 5.290768086125265e-01 5.290768086120402e-01 4.86278e-13 3.60345e-12 ----------------------------------------------------------------------------------------------------- 11 Ga 1 3.678618821430831e+00 3.678618821427966e+00 2.86482e-12 3.16209e-11 2 3.104096409006250e+00 3.104096409000939e+00 5.31086e-12 6.41736e-11 3 2.758421375764033e+00 2.758421375762087e+00 1.94600e-12 3.68554e-11 ----------------------------------------------------------------------------------------------------- 12 N 1 7.484757451158706e-01 7.484757451206113e-01 4.74076e-12 9.50950e-12 2 -8.123387673469296e-02 -8.123387673301125e-02 1.68171e-12 5.53816e-11 3 -5.547398512070144e-01 -5.547398512211477e-01 1.41333e-11 1.19300e-03 * ----------------------------------------------------------------------------------------------------- 13 Ga 1 1.112116463239017e+00 1.112116463237817e+00 1.20015e-12 5.55993e-11 2 4.303510478434828e+00 4.303510478434309e+00 5.18696e-13 2.24656e-11 3 -1.361635564272210e-01 -1.361635564249430e-01 2.27793e-12 3.08823e-11 ----------------------------------------------------------------------------------------------------- 14 N 1 -9.144806450906117e-01 -9.144806450866474e-01 3.96427e-12 4.77252e-12 2 1.446081218745449e+00 1.446081218745068e+00 3.81029e-13 3.14182e-11 3 -2.471523888201922e+00 -2.471523888199386e+00 2.53619e-12 5.64548e-11 ----------------------------------------------------------------------------------------------------- 15 N 1 -6.147026422412730e-01 -6.147026422470393e-01 5.76628e-12 2.05980e-11 2 -2.199306302970229e+00 -2.199306302957479e+00 1.27502e-11 2.04667e-11 3 1.986135522547862e+00 1.986135522544081e+00 3.78053e-12 1.80325e-11 ----------------------------------------------------------------------------------------------------- 16 N 1 4.563109634607901e-01 4.563109634591169e-01 1.67322e-12 1.48708e-11 2 1.055817232988102e+01 1.055817232987233e+01 8.68106e-12 1.17133e-11 3 -1.182329080183919e+01 -1.182329080183910e+01 9.05942e-14 1.26036e-10 ----------------------------------------------------------------------------------------------------- 17 Ga 1 -1.172133124231736e+00 -1.172133124232933e+00 1.19704e-12 1.67462e-09 * 2 -2.314797814978548e+00 -2.314797814979324e+00 7.76268e-13 9.97558e-12 3 -2.126083125769211e+00 -2.126083125769866e+00 6.54587e-13 2.79670e-11 ----------------------------------------------------------------------------------------------------- 18 Ga 1 2.699472820288146e+00 2.699472820286616e+00 1.53033e-12 1.53473e-11 2 2.195456623440859e+00 2.195456623435124e+00 5.73497e-12 1.29194e-11 3 -1.927636186891021e+00 -1.927636186889830e+00 1.19105e-12 8.49101e-11 ----------------------------------------------------------------------------------------------------- 19 Ga 1 2.120230935640799e+00 2.120230935640471e+00 3.27738e-13 3.90523e-11 2 -2.261928302859629e+00 -2.261928302858069e+00 1.55920e-12 3.16547e-12 3 1.393717194129446e+00 1.393717194127808e+00 1.63736e-12 1.02940e-11 ----------------------------------------------------------------------------------------------------- 20 Ga 1 -2.243259699991906e+00 -2.243259699992404e+00 4.97380e-13 1.50551e-11 2 3.300155953012997e+00 3.300155953010747e+00 2.24931e-12 4.31255e-12 3 1.065286024400544e+00 1.065286024401111e+00 5.66880e-13 8.42171e-12 ----------------------------------------------------------------------------------------------------- 21 Ga 1 2.187785103313959e+00 2.187785103314140e+00 1.80300e-13 4.34461e-11 2 -2.107880599991918e+00 -2.107880599997261e+00 5.34239e-12 2.03517e-11 3 7.358603502227223e-01 7.358603502260701e-01 3.34777e-12 4.72936e-11 ----------------------------------------------------------------------------------------------------- 22 N 1 -5.692336733331228e-01 -5.692336733352467e-01 2.12386e-12 1.88449e-11 2 1.136913118878073e-01 1.136913118888820e-01 1.07472e-12 8.68541e-12 3 1.226038290562210e+00 1.226038290562911e+00 7.00773e-13 1.89802e-11 ----------------------------------------------------------------------------------------------------- 23 N 1 -2.521682977069827e+00 -2.521682977070970e+00 1.14309e-12 4.67182e-12 2 1.234771591700165e+00 1.234771591700291e+00 1.25899e-13 9.06741e-12 3 -1.167154312303608e+00 -1.167154312302926e+00 6.81455e-13 4.57745e-12 ----------------------------------------------------------------------------------------------------- 24 Ga 1 -1.134458853400389e+00 -1.134458853400043e+00 3.46168e-13 1.36864e-11 2 -4.478623424363660e+00 -4.478623424358728e+00 4.93117e-12 2.91029e-11 3 1.178201780755734e+00 1.178201780751827e+00 3.90621e-12 3.94285e-12 ----------------------------------------------------------------------------------------------------- 25 N 1 -1.660652439984285e+01 -1.660652439982211e+01 2.07478e-11 2.29569e-10 * 2 1.569057209029170e-01 1.569057209035989e-01 6.81871e-13 1.06528e-10 3 -1.893932019344433e+01 -1.893932019344859e+01 4.26681e-12 7.57225e-11 ----------------------------------------------------------------------------------------------------- 26 Ga 1 -3.244247859915142e+00 -3.244247859909716e+00 5.42677e-12 3.09317e-11 2 -1.714344487080735e+00 -1.714344487085240e+00 4.50529e-12 1.32125e-11 3 -7.524672424519707e-01 -7.524672424493899e-01 2.58082e-12 3.36516e-11 ----------------------------------------------------------------------------------------------------- 27 N 1 1.642487355558755e+01 1.642487355558491e+01 2.64677e-12 1.11754e-10 2 -3.841058167488803e+00 -3.841058167489895e+00 1.09202e-12 1.22133e-11 3 1.476299473301384e+01 1.476299473300652e+01 7.31859e-12 9.40084e-11 ----------------------------------------------------------------------------------------------------- 28 N 1 1.084595917905386e+00 1.084595917905605e+00 2.18492e-13 5.23825e-12 2 3.349709106565186e+00 3.349709106554052e+00 1.11338e-11 1.28590e-11 3 2.312011072271543e+00 2.312011072275296e+00 3.75255e-12 6.35509e-11 ----------------------------------------------------------------------------------------------------- 29 N 1 -1.115120808088019e+00 -1.115120808088468e+00 4.48752e-13 4.08673e-12 2 -9.103202376684893e+00 -9.103202376685687e+00 7.94032e-13 5.03242e-11 3 1.223330012566780e+01 1.223330012566371e+01 4.08740e-12 5.96909e-11 ----------------------------------------------------------------------------------------------------- 30 Ga 1 -2.637367338188000e-01 -2.637367338176395e-01 1.16052e-12 1.09321e-11 2 -2.482626293090222e+00 -2.482626293088803e+00 1.41842e-12 2.79878e-11 3 -1.710061655638968e+00 -1.710061655642495e+00 3.52696e-12 2.05795e-11 ----------------------------------------------------------------------------------------------------- 31 Ga 1 2.114116095549923e+00 2.114116095547812e+00 2.11120e-12 2.33293e-11 2 4.548281814967930e+00 4.548281814969629e+00 1.69909e-12 8.78480e-11 3 -3.175372928816297e+00 -3.175372928818004e+00 1.70752e-12 1.14087e-11 ----------------------------------------------------------------------------------------------------- 32 Ga 1 1.460738651734759e+00 1.460738651737926e+00 3.16658e-12 4.18710e-12 2 -1.343015019459094e+00 -1.343015019456324e+00 2.76956e-12 1.87368e-11 3 1.657464758749712e+00 1.657464758748669e+00 1.04294e-12 2.77596e-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 = 2, direction = 3: |F_model - F_numer| error = ----------------------- = 5.23249e-11 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 3.51837e-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 3.51837e-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.