!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_004 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 6.089485951163533e+00 2.06679e-12 3.76392e-11 2 2.691953275397380e+00 2.691953275401765e+00 4.38494e-12 1.84714e-11 3 2.510907937519865e+00 2.510907937517195e+00 2.67075e-12 2.37068e-11 ----------------------------------------------------------------------------------------------------- 2 Ga 1 -2.569437033826246e+00 -2.569437033842032e+00 1.57860e-11 4.03406e-11 2 -1.498537171250781e+00 -1.498537171258275e+00 7.49423e-12 9.31137e-11 3 3.221179908937704e+00 3.221179908937965e+00 2.61569e-13 2.85825e-11 ----------------------------------------------------------------------------------------------------- 3 Ga 1 -2.025555993868591e+00 -2.025555993870976e+00 2.38520e-12 5.25091e-12 2 2.728750936193485e+00 2.728750936196275e+00 2.78977e-12 8.04752e-11 3 -5.025870094179252e+00 -5.025870094181368e+00 2.11564e-12 2.37081e-11 ----------------------------------------------------------------------------------------------------- 4 Ga 1 3.874855880907573e+00 3.874855880910367e+00 2.79332e-12 1.58500e-11 2 6.956503143758007e-01 6.956503143848868e-01 9.08607e-12 1.14939e-11 3 1.104124705111786e+00 1.104124705109010e+00 2.77578e-12 2.33578e-11 ----------------------------------------------------------------------------------------------------- 5 Ga 1 3.937306088788208e-01 3.937306088795303e-01 7.09488e-13 1.18201e-10 2 2.349765825286505e+00 2.349765825284863e+00 1.64180e-12 4.35505e-11 3 3.564516535253299e+00 3.564516535253007e+00 2.91323e-13 3.91829e-11 ----------------------------------------------------------------------------------------------------- 6 Ga 1 -3.293247047549600e+00 -3.293247047553329e+00 3.72902e-12 3.54885e-11 2 -1.002293161314598e+00 -1.002293161311538e+00 3.05955e-12 6.31972e-11 3 1.466878728997633e+00 1.466878728997765e+00 1.31450e-13 8.96345e-11 ----------------------------------------------------------------------------------------------------- 7 Ga 1 -7.681997212229635e-01 -7.681997212220089e-01 9.54681e-13 5.00074e-11 2 -7.011845005041359e-01 -7.011845005038416e-01 2.94320e-13 3.16474e-11 3 -2.566297805541105e+00 -2.566297805542176e+00 1.07114e-12 3.11644e-11 ----------------------------------------------------------------------------------------------------- 8 Ga 1 -1.267251589120630e+00 -1.267251589121175e+00 5.45342e-13 4.85123e-11 2 -1.592428312632245e+00 -1.592428312636694e+00 4.44866e-12 1.63694e-11 3 -5.976337332814237e-01 -5.976337332836317e-01 2.20801e-12 5.31664e-11 ----------------------------------------------------------------------------------------------------- 9 Ga 1 -2.749303193545896e-01 -2.749303193525490e-01 2.04059e-12 6.45206e-11 2 -1.786512596637748e+00 -1.786512596634770e+00 2.97851e-12 2.87599e-11 3 2.000713265438873e+00 2.000713265443455e+00 4.58122e-12 4.78331e-10 * ----------------------------------------------------------------------------------------------------- 10 Ga 1 -1.637199452346389e+00 -1.637199452347658e+00 1.26898e-12 7.96461e-11 2 -5.756025725900715e-01 -5.756025725927530e-01 2.68152e-12 6.20268e-11 3 2.073838104652293e+00 2.073838104650227e+00 2.06590e-12 7.07256e-11 ----------------------------------------------------------------------------------------------------- 11 Ga 1 -1.264702641297836e+00 -1.264702641300668e+00 2.83196e-12 1.04095e-10 2 -2.185087836852633e+00 -2.185087836855966e+00 3.33245e-12 3.79790e-11 3 -1.193521107580749e+00 -1.193521107584987e+00 4.23794e-12 4.07683e-11 ----------------------------------------------------------------------------------------------------- 12 Ga 1 2.857736513083125e+00 2.857736513081802e+00 1.32250e-12 5.26641e-11 2 -8.933501549354483e-01 -8.933501549383891e-01 2.94076e-12 1.53971e-10 3 -2.155068251451934e+00 -2.155068251447537e+00 4.39782e-12 2.73426e-12 ----------------------------------------------------------------------------------------------------- 13 Ga 1 -1.054032651279646e+00 -1.054032651281572e+00 1.92535e-12 5.99909e-11 2 2.118207367556407e-01 2.118207367495553e-01 6.08538e-12 1.62768e-10 3 -2.386148421989059e+00 -2.386148421991781e+00 2.72182e-12 2.14833e-11 ----------------------------------------------------------------------------------------------------- 14 Ga 1 -9.861808454799790e-01 -9.861808454796455e-01 3.33511e-13 1.17586e-11 2 -3.275254270671228e-01 -3.275254270679885e-01 8.65752e-13 4.02078e-12 3 9.034719129587313e-01 9.034719129648262e-01 6.09490e-12 1.37690e-11 ----------------------------------------------------------------------------------------------------- 15 Ga 1 2.352681575509355e+00 2.352681575501209e+00 8.14637e-12 1.49489e-11 2 4.824681461122549e-01 4.824681461166747e-01 4.41980e-12 6.00408e-11 3 2.621151176823464e+00 2.621151176820400e+00 3.06377e-12 2.90248e-11 ----------------------------------------------------------------------------------------------------- 16 Ga 1 2.308569029269391e+00 2.308569029275913e+00 6.52189e-12 2.21685e-11 2 5.997487533244049e-01 5.997487533270800e-01 2.67508e-12 2.01188e-11 3 1.213988889249468e-01 1.213988889273244e-01 2.37753e-12 2.59053e-11 ----------------------------------------------------------------------------------------------------- 17 Ga 1 1.241981811208290e+00 1.241981811210199e+00 1.90958e-12 1.07336e-11 2 2.046125626799446e+00 2.046125626798022e+00 1.42419e-12 1.86886e-11 3 -1.810732341989230e+00 -1.810732341991758e+00 2.52753e-12 3.31033e-11 ----------------------------------------------------------------------------------------------------- 18 Ga 1 -1.789855045301904e+00 -1.789855045308808e+00 6.90425e-12 8.59357e-12 2 -9.091478230184610e-01 -9.091478230181966e-01 2.64344e-13 2.88879e-11 3 2.092418287842413e+00 2.092418287842386e+00 2.75335e-14 2.80922e-11 ----------------------------------------------------------------------------------------------------- 19 Ga 1 3.061557646183132e+00 3.061557646177287e+00 5.84555e-12 4.76390e-10 * 2 1.323783406172840e+00 1.323783406169061e+00 3.77898e-12 1.23239e-11 3 -1.773828836742637e+00 -1.773828836742496e+00 1.41442e-13 4.10139e-12 ----------------------------------------------------------------------------------------------------- 20 Ga 1 2.118274507856515e+00 2.118274507851992e+00 4.52216e-12 3.68163e-11 2 1.005673711840505e-01 1.005673711836006e-01 4.49973e-13 5.42784e-12 3 -2.129880401201761e+00 -2.129880401203974e+00 2.21290e-12 1.68083e-11 ----------------------------------------------------------------------------------------------------- 21 Ga 1 -3.925343763204227e+00 -3.925343763203962e+00 2.65121e-13 3.17861e-11 2 4.217455439531146e+00 4.217455439528652e+00 2.49401e-12 6.11093e-11 3 5.158725354356689e+00 5.158725354355878e+00 8.10907e-13 5.22853e-11 ----------------------------------------------------------------------------------------------------- 22 Ga 1 -7.411484307880055e-01 -7.411484307823063e-01 5.69922e-12 4.62476e-11 2 1.689117519512635e+00 1.689117519516667e+00 4.03166e-12 2.12774e-11 3 -3.891953502799481e-01 -3.891953502706966e-01 9.25143e-12 7.91335e-11 ----------------------------------------------------------------------------------------------------- 23 Ga 1 -3.300861143557905e+00 -3.300861143558603e+00 6.98552e-13 5.64837e-12 2 2.202171525060445e+00 2.202171525060093e+00 3.52607e-13 1.00924e-11 3 -8.906648892247530e-01 -8.906648892282835e-01 3.53051e-12 9.28979e-12 ----------------------------------------------------------------------------------------------------- 24 Ga 1 3.502135222910076e+00 3.502135222909353e+00 7.22977e-13 1.71121e-11 2 -2.605986567072100e+00 -2.605986567073106e+00 1.00631e-12 4.44356e-12 3 -4.337842428503481e+00 -4.337842428506614e+00 3.13261e-12 1.20773e-10 ----------------------------------------------------------------------------------------------------- 25 Ga 1 2.227317753156537e+00 2.227317753146983e+00 9.55414e-12 3.43565e-11 2 -2.009053149866856e+00 -2.009053149868846e+00 1.99085e-12 7.43094e-12 3 1.719842706218578e+00 1.719842706213551e+00 5.02709e-12 2.18454e-11 ----------------------------------------------------------------------------------------------------- 26 Ga 1 -1.669480546677910e+00 -1.669480546675737e+00 2.17337e-12 9.66298e-11 2 2.684809198319522e-01 2.684809198314084e-01 5.43787e-13 3.24751e-12 3 6.825486121971519e-01 6.825486122016733e-01 4.52138e-12 2.16086e-11 ----------------------------------------------------------------------------------------------------- 27 Ga 1 -1.048618014357744e+00 -1.048618014354192e+00 3.55205e-12 1.73548e-11 2 -1.793300918057738e+00 -1.793300918055179e+00 2.55906e-12 8.31468e-12 3 -5.487322294328751e-01 -5.487322294352672e-01 2.39209e-12 2.52999e-11 ----------------------------------------------------------------------------------------------------- 28 Ga 1 6.280881983825830e-01 6.280881983782018e-01 4.38116e-12 1.11526e-11 2 -7.566585102744999e-02 -7.566585102903987e-02 1.58988e-12 5.42721e-12 3 -2.481682465844736e+00 -2.481682465845252e+00 5.16032e-13 3.05680e-11 ----------------------------------------------------------------------------------------------------- 29 Ga 1 1.110012189742885e+00 1.110012189740901e+00 1.98441e-12 2.10110e-11 2 1.741566388848462e-01 1.741566388841064e-01 7.39742e-13 9.07551e-11 3 9.026800075952246e-03 9.026800072776285e-03 3.17596e-12 5.14478e-11 ----------------------------------------------------------------------------------------------------- 30 Ga 1 -2.429979091804984e+00 -2.429979091805321e+00 3.37952e-13 7.76890e-12 2 -1.776098357046361e+00 -1.776098357048099e+00 1.73728e-12 6.68106e-11 3 -1.485092368244212e+00 -1.485092368245303e+00 1.09046e-12 2.41753e-11 ----------------------------------------------------------------------------------------------------- 31 Ga 1 -2.742280880794121e+00 -2.742280880786176e+00 7.94520e-12 3.72022e-11 2 -2.715999274484886e+00 -2.715999274482481e+00 2.40474e-12 2.87872e-11 3 1.375173130656759e-01 1.375173130676948e-01 2.01891e-12 7.25286e-12 ----------------------------------------------------------------------------------------------------- 32 Ga 1 1.021877323579394e+00 1.021877323578530e+00 8.64420e-13 2.77001e-12 2 6.657572399357885e-01 6.657572399352527e-01 5.35794e-13 5.12612e-12 3 3.839304871121105e-01 3.839304871114697e-01 6.40821e-13 6.49653e-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 2.229017231993385e+00 5.79536e-13 1.20570e-12 2 1.676068406799527e+00 1.676068406801332e+00 1.80456e-12 3.13882e-12 3 3.392603824650414e+00 3.392603824651448e+00 1.03428e-12 1.31419e-11 ----------------------------------------------------------------------------------------------------- 2 N 1 -1.572449312886381e+00 -1.572449312886830e+00 4.49640e-13 7.78533e-12 2 5.523023936399424e-01 5.523023936366456e-01 3.29681e-12 3.88634e-12 3 -4.580706135413844e-01 -4.580706135429263e-01 1.54188e-12 1.56943e-11 ----------------------------------------------------------------------------------------------------- 3 N 1 3.548315956446321e-01 3.548315956456882e-01 1.05610e-12 8.77959e-12 2 -4.921597847658496e-01 -4.921597847630843e-01 2.76534e-12 3.17907e-11 3 -3.296630873322994e+00 -3.296630873319765e+00 3.22897e-12 1.06897e-11 ----------------------------------------------------------------------------------------------------- 4 N 1 -2.108237696421435e+00 -2.108237696422097e+00 6.62137e-13 6.17297e-11 2 1.710149633696747e+00 1.710149633692216e+00 4.53104e-12 1.39559e-11 3 -8.361402466805178e-01 -8.361402466830821e-01 2.56428e-12 4.33996e-11 ----------------------------------------------------------------------------------------------------- 5 N 1 -1.681554026824143e+00 -1.681554026824813e+00 6.70575e-13 3.06977e-12 2 -9.478658981991062e-01 -9.478658981997620e-01 6.55809e-13 1.02350e-11 3 3.132397511716968e+00 3.132397511719575e+00 2.60725e-12 8.76765e-12 ----------------------------------------------------------------------------------------------------- 6 N 1 -3.199151008675044e+00 -3.199151008675238e+00 1.94067e-13 1.95546e-11 2 4.702875244802402e-01 4.702875244807009e-01 4.60687e-13 7.74547e-12 3 3.133451364709507e+00 3.133451364709632e+00 1.24789e-13 9.56524e-12 ----------------------------------------------------------------------------------------------------- 7 N 1 -3.369963675785457e+00 -3.369963675786657e+00 1.19993e-12 1.39209e-11 2 3.637433041427253e+00 3.637433041428540e+00 1.28697e-12 3.62150e-11 3 -3.602018781277854e-01 -3.602018781269688e-01 8.16569e-13 9.46349e-12 ----------------------------------------------------------------------------------------------------- 8 N 1 6.910190996704113e+00 6.910190996705312e+00 1.19904e-12 7.50138e-11 2 -4.831622160721856e+00 -4.831622160726437e+00 4.58122e-12 4.80975e-11 3 -8.323908640679883e-01 -8.323908640671848e-01 8.03579e-13 1.11525e-10 ----------------------------------------------------------------------------------------------------- 9 N 1 1.228912015253321e+00 1.228912015254648e+00 1.32694e-12 1.75249e-11 2 -1.655043504633467e+00 -1.655043504631109e+00 2.35811e-12 7.34923e-12 3 5.422095930446078e-01 5.422095930449895e-01 3.81695e-13 7.57971e-12 ----------------------------------------------------------------------------------------------------- 10 N 1 6.060189520941317e-01 6.060189520927618e-01 1.36990e-12 6.35447e-12 2 -1.562957312028991e+00 -1.562957312029039e+00 4.79616e-14 4.96958e-12 3 2.631677428612464e+00 2.631677428613152e+00 6.88338e-13 6.28120e-12 ----------------------------------------------------------------------------------------------------- 11 N 1 -3.184326591295067e+00 -3.184326591292532e+00 2.53531e-12 9.88454e-12 2 1.415927190000242e+00 1.415927189999880e+00 3.61933e-13 1.68696e-11 3 -2.207726488332600e+00 -2.207726488330457e+00 2.14317e-12 9.46887e-12 ----------------------------------------------------------------------------------------------------- 12 N 1 2.227265776873083e+00 2.227265776868593e+00 4.49063e-12 2.39448e-11 2 -1.551163622515998e+00 -1.551163622516189e+00 1.90736e-13 4.34763e-12 3 3.172196547929959e+00 3.172196547930994e+00 1.03562e-12 2.47296e-11 ----------------------------------------------------------------------------------------------------- 13 N 1 3.450210558718039e+00 3.450210558724383e+00 6.34337e-12 2.99822e-11 2 -7.419173110554119e-01 -7.419173110574049e-01 1.99296e-12 8.38241e-12 3 -1.599452074733638e+00 -1.599452074734690e+00 1.05160e-12 1.90249e-10 * ----------------------------------------------------------------------------------------------------- 14 N 1 -6.008825991286131e-01 -6.008825991276510e-01 9.62119e-13 3.82826e-11 2 -3.520139818802436e-02 -3.520139818784980e-02 1.74562e-13 1.07542e-12 3 -4.939425943903832e-01 -4.939425943900377e-01 3.45501e-13 2.46392e-12 ----------------------------------------------------------------------------------------------------- 15 N 1 1.144665967625631e+00 1.144665967622545e+00 3.08531e-12 8.54961e-12 2 -1.250193756023604e+00 -1.250193756019489e+00 4.11471e-12 8.18783e-11 3 2.452183924909368e-01 2.452183924926750e-01 1.73817e-12 1.11461e-11 ----------------------------------------------------------------------------------------------------- 16 N 1 -1.288959880485184e+00 -1.288959880483477e+00 1.70708e-12 1.62017e-11 2 2.542226431876976e+00 2.542226431873928e+00 3.04823e-12 1.59726e-11 3 -1.101077531348745e+00 -1.101077531343726e+00 5.01910e-12 2.17719e-11 ----------------------------------------------------------------------------------------------------- 17 N 1 3.169989913529601e+00 3.169989913528962e+00 6.39933e-13 1.98410e-11 2 1.479626805435628e+00 1.479626805435240e+00 3.88578e-13 2.28682e-11 3 -2.142498705382576e-02 -2.142498705809283e-02 4.26707e-12 5.92958e-11 ----------------------------------------------------------------------------------------------------- 18 N 1 -1.994551754001229e+00 -1.994551754011899e+00 1.06708e-11 2.88194e-11 2 -2.228475099885045e+00 -2.228475099883950e+00 1.09512e-12 2.80931e-11 3 1.156980977045035e+00 1.156980977042774e+00 2.26130e-12 1.31601e-11 ----------------------------------------------------------------------------------------------------- 19 N 1 -5.454238005110048e-01 -5.454238005076895e-01 3.31535e-12 5.88242e-11 2 2.757345173141988e+00 2.757345173151897e+00 9.90896e-12 4.29226e-11 3 -1.718533766280997e+00 -1.718533766276471e+00 4.52571e-12 4.26505e-11 ----------------------------------------------------------------------------------------------------- 20 N 1 2.011310823883059e+00 2.011310823883542e+00 4.82725e-13 3.19873e-11 2 -1.280339095547168e+00 -1.280339095547015e+00 1.52545e-13 1.07503e-11 3 -1.000897682112259e+00 -1.000897682115266e+00 3.00737e-12 2.25069e-11 ----------------------------------------------------------------------------------------------------- 21 N 1 6.991913435365302e-01 6.991913435356509e-01 8.79297e-13 5.40571e-11 2 1.795285833360196e+00 1.795285833358307e+00 1.88960e-12 2.65714e-11 3 1.363978113705661e+00 1.363978113705125e+00 5.35350e-13 1.07767e-11 ----------------------------------------------------------------------------------------------------- 22 N 1 -1.363578936733544e+00 -1.363578936732369e+00 1.17484e-12 5.29177e-11 2 2.106350682371910e+00 2.106350682375532e+00 3.62155e-12 3.48246e-11 3 5.865644843145479e-01 5.865644843143721e-01 1.75748e-13 4.25315e-12 ----------------------------------------------------------------------------------------------------- 23 N 1 -3.799545991950590e+00 -3.799545991949299e+00 1.29052e-12 1.33475e-11 2 2.085901214529002e+00 2.085901214528983e+00 1.86517e-14 7.10276e-12 3 -1.836541147261561e+00 -1.836541147261380e+00 1.81188e-13 2.02465e-11 ----------------------------------------------------------------------------------------------------- 24 N 1 1.619134298208803e+00 1.619134298210062e+00 1.25921e-12 6.40641e-11 2 -4.186371938056291e+00 -4.186371938057277e+00 9.85878e-13 3.95319e-11 3 1.029722725562884e-01 1.029722725584531e-01 2.16471e-12 9.84542e-11 ----------------------------------------------------------------------------------------------------- 25 N 1 3.444940940237883e-01 3.444940940217551e-01 2.03315e-12 2.95804e-11 2 -9.124416369144561e-01 -9.124416369119357e-01 2.52043e-12 9.76463e-12 3 -1.891979104895945e+00 -1.891979104897382e+00 1.43641e-12 4.33191e-11 ----------------------------------------------------------------------------------------------------- 26 N 1 -2.841087543677121e+00 -2.841087543677483e+00 3.62821e-13 7.95151e-11 2 3.653550515548775e-01 3.653550515561730e-01 1.29557e-12 2.04305e-11 3 1.117722603843336e+00 1.117722603842246e+00 1.08979e-12 1.17248e-11 ----------------------------------------------------------------------------------------------------- 27 N 1 -8.722198617861476e-01 -8.722198617887333e-01 2.58571e-12 1.07290e-11 2 3.704938119728200e+00 3.704938119726730e+00 1.47038e-12 3.39808e-11 3 -6.420954695550579e-01 -6.420954695562032e-01 1.14531e-12 4.87677e-12 ----------------------------------------------------------------------------------------------------- 28 N 1 4.006950214503809e+00 4.006950214502931e+00 8.78408e-13 3.07390e-11 2 -1.616126362195088e+00 -1.616126362191425e+00 3.66240e-12 1.23968e-11 3 -2.357777658963388e+00 -2.357777658969014e+00 5.62572e-12 3.98508e-11 ----------------------------------------------------------------------------------------------------- 29 N 1 1.654163873605881e-01 1.654163873600326e-01 5.55556e-13 4.27796e-11 2 4.456722053947461e-01 4.456722053957847e-01 1.03861e-12 9.39671e-12 3 1.711136091207596e+00 1.711136091204494e+00 3.10130e-12 5.19620e-11 ----------------------------------------------------------------------------------------------------- 30 N 1 -1.146414939510601e+00 -1.146414939512580e+00 1.97886e-12 2.80069e-11 2 -7.999706399201908e-01 -7.999706399179108e-01 2.27995e-12 2.84522e-11 3 2.371378351643068e+00 2.371378351651599e+00 8.53140e-12 7.76632e-11 ----------------------------------------------------------------------------------------------------- 31 N 1 2.313443789250394e-01 2.313443789266071e-01 1.56766e-12 9.30108e-11 2 1.788477276862484e-01 1.788477276820841e-01 4.16431e-12 1.59942e-11 3 -2.939963746970566e+00 -2.939963746964408e+00 6.15819e-12 4.26610e-11 ----------------------------------------------------------------------------------------------------- 32 N 1 -8.305969292065721e-01 -8.305969292078605e-01 1.28841e-12 1.64966e-10 * 2 -2.831867914473172e+00 -2.831867914474409e+00 1.23768e-12 2.18052e-11 3 -1.065640829830756e+00 -1.065640829831284e+00 5.28244e-13 1.62002e-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 9.702877969940974e-01 3.43392e-13 8.71858e-13 2 1.336133179495352e+00 1.336133179494899e+00 4.52305e-13 1.77820e-11 3 -3.530469525592479e-01 -3.530469525597758e-01 5.27911e-13 4.38644e-12 ----------------------------------------------------------------------------------------------------- 2 N 1 -1.499776796628493e+00 -1.499776796627524e+00 9.68781e-13 2.21627e-11 2 -1.778452560451200e+00 -1.778452560451217e+00 1.64313e-14 7.39941e-11 3 -4.050547523101215e-02 -4.050547523313162e-02 2.11947e-12 1.41425e-11 ----------------------------------------------------------------------------------------------------- 3 N 1 -7.031777562241026e+00 -7.031777562240365e+00 6.60805e-13 8.72440e-11 2 -5.976657949319230e+00 -5.976657949316752e+00 2.47802e-12 1.23508e-10 3 2.464725363123677e+00 2.464725363127688e+00 4.01190e-12 2.49614e-11 ----------------------------------------------------------------------------------------------------- 4 Ga 1 -1.928347480553567e+00 -1.928347480549321e+00 4.24571e-12 6.07041e-11 2 -1.732371378341726e+00 -1.732371378343498e+00 1.77236e-12 6.23990e-12 3 8.854413461719519e-01 8.854413461746633e-01 2.71139e-12 2.71493e-11 ----------------------------------------------------------------------------------------------------- 5 N 1 2.245634147194882e+00 2.245634147195303e+00 4.21441e-13 1.38751e-11 2 -1.201501678531007e+01 -1.201501678530291e+01 7.15517e-12 1.66603e-10 3 -1.337398134684897e+01 -1.337398134682106e+01 2.79137e-11 1.31886e-10 ----------------------------------------------------------------------------------------------------- 6 Ga 1 1.922237716658862e-01 1.922237716724149e-01 6.52869e-12 1.68257e-11 2 -2.344920533308638e+00 -2.344920533310280e+00 1.64224e-12 2.01323e-11 3 2.176907569104704e+00 2.176907569104003e+00 7.01217e-13 1.02736e-10 ----------------------------------------------------------------------------------------------------- 7 Ga 1 4.485940344983474e-01 4.485940344977006e-01 6.46871e-13 4.39692e-11 2 1.990609682435883e+00 1.990609682434788e+00 1.09490e-12 6.43057e-11 3 1.127202210380217e+00 1.127202210373797e+00 6.42042e-12 1.06291e-11 ----------------------------------------------------------------------------------------------------- 8 N 1 4.175762403893491e+00 4.175762403897765e+00 4.27391e-12 6.62483e-11 2 1.899800974968928e+01 1.899800974969211e+01 2.82796e-12 2.40238e-10 * 3 1.213432381315724e+01 1.213432381315452e+01 2.71605e-12 1.02158e-10 ----------------------------------------------------------------------------------------------------- 9 Ga 1 -1.566664287274916e+00 -1.566664287273833e+00 1.08313e-12 2.15776e-11 2 1.398982810460669e+00 1.398982810456073e+00 4.59566e-12 4.31633e-12 3 -2.075760821005730e+00 -2.075760821006247e+00 5.16920e-13 3.07043e-12 ----------------------------------------------------------------------------------------------------- 10 N 1 3.063103162082931e-01 3.063103162124908e-01 4.19775e-12 6.26244e-12 2 -2.259132108193293e+00 -2.259132108189116e+00 4.17666e-12 2.35940e-11 3 5.290768086125265e-01 5.290768086120405e-01 4.85945e-13 3.60323e-12 ----------------------------------------------------------------------------------------------------- 11 Ga 1 3.678618821430831e+00 3.678618821427968e+00 2.86260e-12 3.16218e-11 2 3.104096409006250e+00 3.104096409000940e+00 5.30953e-12 6.41736e-11 3 2.758421375764033e+00 2.758421375762088e+00 1.94467e-12 3.68559e-11 ----------------------------------------------------------------------------------------------------- 12 N 1 7.484757451158706e-01 7.484757451206117e-01 4.74110e-12 9.50984e-12 2 -8.123387673469296e-02 -8.123387673301131e-02 1.68164e-12 5.53817e-11 3 -5.547398512070144e-01 -5.547398512211474e-01 1.41330e-11 1.19300e-03 * ----------------------------------------------------------------------------------------------------- 13 Ga 1 1.112116463239017e+00 1.112116463237818e+00 1.19904e-12 5.55989e-11 2 4.303510478434828e+00 4.303510478434312e+00 5.16032e-13 2.24656e-11 3 -1.361635564272210e-01 -1.361635564249431e-01 2.27784e-12 3.08823e-11 ----------------------------------------------------------------------------------------------------- 14 N 1 -9.144806450906117e-01 -9.144806450866479e-01 3.96372e-12 4.77218e-12 2 1.446081218745449e+00 1.446081218745067e+00 3.81695e-13 3.14178e-11 3 -2.471523888201922e+00 -2.471523888199385e+00 2.53753e-12 5.64553e-11 ----------------------------------------------------------------------------------------------------- 15 N 1 -6.147026422412730e-01 -6.147026422470390e-01 5.76594e-12 2.05982e-11 2 -2.199306302970229e+00 -2.199306302957480e+00 1.27489e-11 2.04654e-11 3 1.986135522547862e+00 1.986135522544080e+00 3.78142e-12 1.80331e-11 ----------------------------------------------------------------------------------------------------- 16 N 1 4.563109634607901e-01 4.563109634591166e-01 1.67349e-12 1.48709e-11 2 1.055817232988102e+01 1.055817232987234e+01 8.67395e-12 1.17168e-11 3 -1.182329080183919e+01 -1.182329080183909e+01 9.41469e-14 1.26029e-10 ----------------------------------------------------------------------------------------------------- 17 Ga 1 -1.172133124231736e+00 -1.172133124232933e+00 1.19749e-12 1.67462e-09 * 2 -2.314797814978548e+00 -2.314797814979323e+00 7.75380e-13 9.97558e-12 3 -2.126083125769211e+00 -2.126083125769865e+00 6.53699e-13 2.79679e-11 ----------------------------------------------------------------------------------------------------- 18 Ga 1 2.699472820288146e+00 2.699472820286614e+00 1.53211e-12 1.53477e-11 2 2.195456623440859e+00 2.195456623435120e+00 5.73808e-12 1.29230e-11 3 -1.927636186891021e+00 -1.927636186889832e+00 1.18971e-12 8.49101e-11 ----------------------------------------------------------------------------------------------------- 19 Ga 1 2.120230935640799e+00 2.120230935640470e+00 3.28626e-13 3.90532e-11 2 -2.261928302859629e+00 -2.261928302858056e+00 1.57252e-12 3.18012e-12 3 1.393717194129446e+00 1.393717194127808e+00 1.63780e-12 1.02940e-11 ----------------------------------------------------------------------------------------------------- 20 Ga 1 -2.243259699991906e+00 -2.243259699992402e+00 4.96048e-13 1.50560e-11 2 3.300155953012997e+00 3.300155953010749e+00 2.24754e-12 4.31122e-12 3 1.065286024400544e+00 1.065286024401112e+00 5.67768e-13 8.42237e-12 ----------------------------------------------------------------------------------------------------- 21 Ga 1 2.187785103313959e+00 2.187785103314138e+00 1.78968e-13 4.34457e-11 2 -2.107880599991918e+00 -2.107880599997259e+00 5.34106e-12 2.03517e-11 3 7.358603502227223e-01 7.358603502260698e-01 3.34743e-12 4.72932e-11 ----------------------------------------------------------------------------------------------------- 22 N 1 -5.692336733331228e-01 -5.692336733347907e-01 1.66789e-12 2.28254e-11 2 1.136913118878073e-01 1.136913118888821e-01 1.07481e-12 8.68540e-12 3 1.226038290562210e+00 1.226038290562912e+00 7.01661e-13 1.89795e-11 ----------------------------------------------------------------------------------------------------- 23 N 1 -2.521682977069827e+00 -2.521682977070972e+00 1.14486e-12 4.67093e-12 2 1.234771591700165e+00 1.234771591700292e+00 1.26565e-13 9.06941e-12 3 -1.167154312303608e+00 -1.167154312302927e+00 6.80789e-13 4.57767e-12 ----------------------------------------------------------------------------------------------------- 24 Ga 1 -1.134458853400389e+00 -1.134458853400044e+00 3.45279e-13 1.36866e-11 2 -4.478623424363660e+00 -4.478623424358733e+00 4.92673e-12 2.91012e-11 3 1.178201780755734e+00 1.178201780751828e+00 3.90532e-12 3.94329e-12 ----------------------------------------------------------------------------------------------------- 25 N 1 -1.660652439984285e+01 -1.660652439982210e+01 2.07585e-11 2.29583e-10 * 2 1.569057209029170e-01 1.569057209035990e-01 6.82010e-13 1.06528e-10 3 -1.893932019344433e+01 -1.893932019344861e+01 4.28102e-12 7.57261e-11 ----------------------------------------------------------------------------------------------------- 26 Ga 1 -3.244247859915142e+00 -3.244247859909714e+00 5.42810e-12 3.09313e-11 2 -1.714344487080735e+00 -1.714344487085241e+00 4.50640e-12 1.32134e-11 3 -7.524672424519707e-01 -7.524672424493896e-01 2.58116e-12 3.36521e-11 ----------------------------------------------------------------------------------------------------- 27 N 1 1.642487355558755e+01 1.642487355558490e+01 2.65388e-12 1.11754e-10 2 -3.841058167488803e+00 -3.841058167489898e+00 1.09468e-12 1.22133e-11 3 1.476299473301384e+01 1.476299473300653e+01 7.30971e-12 9.40155e-11 ----------------------------------------------------------------------------------------------------- 28 N 1 1.084595917905386e+00 1.084595917905605e+00 2.19158e-13 5.23892e-12 2 3.349709106565186e+00 3.349709106554054e+00 1.11315e-11 1.28599e-11 3 2.312011072271543e+00 2.312011072275295e+00 3.75167e-12 6.35523e-11 ----------------------------------------------------------------------------------------------------- 29 N 1 -1.115120808088019e+00 -1.115120808088469e+00 4.49418e-13 4.08762e-12 2 -9.103202376684893e+00 -9.103202376685696e+00 8.02913e-13 5.03206e-11 3 1.223330012566780e+01 1.223330012566372e+01 4.07674e-12 5.96980e-11 ----------------------------------------------------------------------------------------------------- 30 Ga 1 -2.637367338188000e-01 -2.637367338176393e-01 1.16068e-12 1.09322e-11 2 -2.482626293090222e+00 -2.482626293088805e+00 1.41664e-12 2.79927e-11 3 -1.710061655638968e+00 -1.710061655642494e+00 3.52607e-12 2.05795e-11 ----------------------------------------------------------------------------------------------------- 31 Ga 1 2.114116095549923e+00 2.114116095547812e+00 2.11031e-12 2.33298e-11 2 4.548281814967930e+00 4.548281814969632e+00 1.70264e-12 8.78488e-11 3 -3.175372928816297e+00 -3.175372928818003e+00 1.70619e-12 1.14087e-11 ----------------------------------------------------------------------------------------------------- 32 Ga 1 1.460738651734759e+00 1.460738651737927e+00 3.16769e-12 4.18843e-12 2 -1.343015019459094e+00 -1.343015019456325e+00 2.76867e-12 1.87359e-11 3 1.657464758749712e+00 1.657464758748670e+00 1.04183e-12 2.77613e-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 = ----------------------- = 5.23255e-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.