!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : Sim_LAMMPS_Polymorphic_Zhou_2004_CuTa__SM_453737875254_000 Supported species : Cu Ta 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 = Cu | a0 = 3.6149597168 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 4.717999227187883e-01 4.717999227410654e-01 2.22771e-11 1.51577e-09 2 1.488332774721404e-01 1.488332775617189e-01 8.95785e-11 1.44575e-09 3 -1.135762042181385e-01 -1.135762042228460e-01 4.70746e-12 7.54971e-11 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -4.416471659663069e-01 -4.416471655312855e-01 4.35021e-10 2.23278e-09 2 9.249880091627981e-01 9.249880092061797e-01 4.33816e-11 3.27986e-10 3 8.430344093285024e-01 8.430344093344750e-01 5.97267e-12 2.52233e-10 ----------------------------------------------------------------------------------------------------- 3 Cu 1 2.175201568380133e-01 2.175201571619173e-01 3.23904e-10 1.54931e-09 2 8.583219173305903e-01 8.583219166847760e-01 6.45814e-10 2.94830e-09 3 1.034844739435346e+00 1.034844739534041e+00 9.86948e-11 4.05335e-10 ----------------------------------------------------------------------------------------------------- 4 Cu 1 8.806988193595853e-01 8.806988193236958e-01 3.58895e-11 7.83583e-10 2 3.217805211749148e-01 3.217805214278433e-01 2.52928e-10 2.81351e-09 3 8.547744125176719e-01 8.547744125516343e-01 3.39624e-11 1.66699e-09 ----------------------------------------------------------------------------------------------------- 5 Cu 1 3.030848243013036e-01 3.030848241253493e-01 1.75954e-10 2.64340e-10 2 3.227358640006376e-01 3.227358638837093e-01 1.16928e-10 1.22153e-09 3 1.386628646194765e-01 1.386628650625492e-01 4.43073e-10 1.88900e-09 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -1.055185523758791e+00 -1.055185523819086e+00 6.02953e-11 3.60732e-10 2 4.785994627603524e-01 4.785994626675162e-01 9.28362e-11 8.19541e-11 3 9.567580719770065e-01 9.567580718010418e-01 1.75965e-10 2.53623e-09 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.536641775781534e+00 1.536641775632512e+00 1.49023e-10 2.51021e-09 2 -2.610317377619580e+00 -2.610317377592563e+00 2.70175e-11 1.30667e-09 3 -3.143877248998768e+00 -3.143877249849393e+00 8.50626e-10 6.72480e-09 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -2.613089089196711e+00 -2.613089085005659e+00 4.19105e-09 1.94051e-08 * 2 -7.389940296964311e-01 -7.389940298536500e-01 1.57219e-10 8.74940e-10 3 -5.197234903093454e-01 -5.197234847219980e-01 5.58735e-09 6.74633e-09 ----------------------------------------------------------------------------------------------------- 9 Cu 1 9.525041987046690e-02 9.525041929924184e-02 5.71225e-10 4.19340e-09 2 -2.324096331219185e+00 -2.324096330872598e+00 3.46587e-10 7.95100e-10 3 -1.945796671825114e+00 -1.945796670992756e+00 8.32358e-10 7.92731e-10 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -1.200870390631028e+00 -1.200870390897348e+00 2.66320e-10 4.42201e-10 2 1.332504652998161e+00 1.332504652942892e+00 5.52687e-11 5.24334e-10 3 -1.790938623397651e+00 -1.790938623516097e+00 1.18446e-10 1.03911e-09 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -4.601768757714726e-01 -4.601768758134573e-01 4.19847e-11 6.74008e-09 2 -2.457595708104799e+00 -2.457595708087899e+00 1.68998e-11 4.98170e-08 * 3 1.451629249965293e+00 1.451629250645816e+00 6.80523e-10 1.18401e-09 ----------------------------------------------------------------------------------------------------- 12 Cu 1 2.249753819582552e-01 2.249753820874465e-01 1.29191e-10 3.52697e-09 2 2.322164884979228e+00 2.322164884546333e+00 4.32896e-10 1.01068e-09 3 1.591001180258147e+00 1.591001180053101e+00 2.05046e-10 1.91819e-09 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -1.093022179615642e+00 -1.093022178582816e+00 1.03283e-09 1.05814e-08 2 -2.583209994476299e+00 -2.583209996559193e+00 2.08289e-09 4.40333e-09 3 -3.888247755127664e+00 -3.888247755259619e+00 1.31954e-10 3.36849e-09 ----------------------------------------------------------------------------------------------------- 14 Cu 1 1.957806220432616e-01 1.957806219777823e-01 6.54793e-11 2.94091e-09 2 8.137557215412086e-01 8.137557219350245e-01 3.93816e-10 3.10421e-08 * 3 -1.909458006483581e-01 -1.909458006767560e-01 2.83979e-11 9.51316e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 3.596161434409610e+00 3.596161433145268e+00 1.26434e-09 3.14695e-09 2 -7.233166443911475e-01 -7.233166450162436e-01 6.25096e-10 1.41821e-09 3 2.100106893329797e+00 2.100106891003175e+00 2.32662e-09 1.11838e-07 * ----------------------------------------------------------------------------------------------------- 16 Cu 1 1.087384920188615e+00 1.087384919780734e+00 4.07880e-10 8.12846e-10 2 2.866753743711928e+00 2.866753745008405e+00 1.29648e-09 8.48973e-09 3 1.747647479099804e+00 1.747647479911797e+00 8.11994e-10 4.79983e-09 ----------------------------------------------------------------------------------------------------- 17 Cu 1 6.012112259580727e-01 6.012112258458374e-01 1.12235e-10 2.38040e-10 2 4.597383616597139e-01 4.597383616672402e-01 7.52631e-12 8.86060e-10 3 -4.324948262264269e-01 -4.324948263758027e-01 1.49376e-10 1.62696e-09 ----------------------------------------------------------------------------------------------------- 18 Cu 1 6.626542423127891e-01 6.626542421488196e-01 1.63970e-10 5.89898e-10 2 5.648139542292304e-01 5.648139544063970e-01 1.77167e-10 3.21447e-10 3 -1.028404167372932e+00 -1.028404167365530e+00 7.40208e-12 2.08273e-09 ----------------------------------------------------------------------------------------------------- 19 Cu 1 3.415054930036505e-01 3.415054930926265e-01 8.89759e-11 1.23369e-09 2 4.728878982612897e-01 4.728878983355224e-01 7.42327e-11 2.32600e-08 * 3 -6.077390125100850e-01 -6.077390126365155e-01 1.26431e-10 1.98707e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 5.647962986441121e-01 5.647963001258607e-01 1.48175e-09 4.11902e-08 * 2 5.440730144970857e-01 5.440730144353768e-01 6.17089e-11 1.10860e-09 3 -4.694550609887035e-01 -4.694550618583359e-01 8.69632e-10 2.81667e-09 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -2.158975920673742e+00 -2.158975927633262e+00 6.95952e-09 7.38674e-09 2 2.191237219055364e-01 2.191237300142459e-01 8.10871e-09 1.20138e-08 3 1.812497506233880e+00 1.812497505824085e+00 4.09795e-10 3.18433e-09 ----------------------------------------------------------------------------------------------------- 22 Cu 1 7.691593248567942e-01 7.691593245236024e-01 3.33192e-10 1.87892e-09 2 2.394702314771652e+00 2.394702314357255e+00 4.14396e-10 8.47113e-09 3 2.118046632777919e+00 2.118046632512484e+00 2.65435e-10 7.64241e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -8.343878883203472e-01 -8.343878889417972e-01 6.21450e-10 2.48236e-09 2 7.423173464049918e-01 7.423173480184421e-01 1.61345e-09 9.64671e-10 3 -6.173970648343569e-01 -6.173970647536043e-01 8.07525e-11 1.45011e-09 ----------------------------------------------------------------------------------------------------- 24 Cu 1 1.576227105558060e-01 1.576227099789125e-01 5.76893e-10 1.19824e-09 2 1.197913412055263e-01 1.197913414107874e-01 2.05261e-10 2.41964e-10 3 -1.020551603515278e+00 -1.020551602596248e+00 9.19030e-10 5.57534e-09 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -7.762882395995173e-01 -7.762882317442752e-01 7.85524e-09 1.27837e-08 * 2 -1.357182171550208e+00 -1.357182177249280e+00 5.69907e-09 1.04642e-08 3 6.206525973980274e-01 6.206525966068958e-01 7.91132e-10 1.00738e-08 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -3.583832859551775e-01 -3.583832858296945e-01 1.25483e-10 9.47800e-10 2 1.985318205131140e+00 1.985318205474448e+00 3.43308e-10 1.20902e-09 3 -1.681481719762973e+00 -1.681481719676054e+00 8.69198e-11 6.54446e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 1.410633984026972e+00 1.410633983800979e+00 2.25993e-10 3.12533e-09 2 -4.232572093935844e+00 -4.232572094514690e+00 5.78845e-10 3.91739e-09 3 1.440028095392345e+00 1.440028095249515e+00 1.42830e-10 9.33738e-10 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -1.281453605909735e+00 -1.281453605713259e+00 1.96477e-10 1.97703e-10 2 1.197126454611757e+00 1.197126454898705e+00 2.86948e-10 1.78776e-09 3 -2.508467868476490e-01 -2.508467870658920e-01 2.18243e-10 2.16773e-09 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -8.858912843707181e-01 -8.858912841926092e-01 1.78109e-10 9.95493e-10 2 -1.054546989606019e+00 -1.054546990070744e+00 4.64725e-10 5.44358e-09 3 1.247174907630437e+00 1.247174904823677e+00 2.80676e-09 4.15888e-09 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -6.892661513362383e-01 -6.892661512800762e-01 5.61621e-11 3.88145e-09 2 9.551599368383551e-01 9.551599366548820e-01 1.83473e-10 1.11555e-09 3 -1.349051736670563e+00 -1.349051736501286e+00 1.69277e-10 1.09330e-09 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -3.361417921907492e-02 -3.361417927160428e-02 5.25294e-11 1.26114e-09 2 -2.059577319423005e+00 -2.059577319080938e+00 3.42067e-10 2.46813e-09 3 1.200613586360669e+00 1.200613586443197e+00 8.25287e-11 3.07580e-09 ----------------------------------------------------------------------------------------------------- 32 Cu 1 7.653702234968727e-01 7.653702234902580e-01 6.61471e-12 2.04256e-09 2 9.591805537428227e-02 9.591805552827118e-02 1.53989e-10 1.83174e-09 3 -1.069448530703125e-01 -1.069448532925640e-01 2.22252e-10 3.18647e-09 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 21, direction = 2: |F_model - F_numer| error = ----------------------- = 3.70052e-08 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Ta | a0 = 4.14023113251 | (Configuration in file "config-Ta.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ta 1 4.355392547636326e-01 4.355392547906854e-01 2.70527e-11 1.18095e-09 2 1.457814357924129e+00 1.457814357747844e+00 1.76285e-10 7.66615e-10 3 1.153877456487743e+00 1.153877456520470e+00 3.27267e-11 1.71665e-09 ----------------------------------------------------------------------------------------------------- 2 Ta 1 1.073115779291839e-01 1.073115778014463e-01 1.27738e-10 7.55253e-09 2 -2.189520867208631e-01 -2.189520859729421e-01 7.47921e-10 3.77977e-09 3 8.852035370275988e-01 8.852035370509842e-01 2.33854e-11 3.35812e-09 ----------------------------------------------------------------------------------------------------- 3 Ta 1 1.042871314088898e+00 1.042871313544009e+00 5.44889e-10 5.77169e-08 2 9.181261760284078e-01 9.181261749192610e-01 1.10915e-09 2.60841e-09 3 7.427702553584459e-01 7.427702557385667e-01 3.80121e-10 2.09286e-08 ----------------------------------------------------------------------------------------------------- 4 Ta 1 1.094585151070709e+00 1.094585150525601e+00 5.45108e-10 3.96417e-09 2 1.227412308344638e+00 1.227412308385865e+00 4.12268e-11 1.43156e-07 * 3 -1.816008999401734e+00 -1.816008999552407e+00 1.50674e-10 2.93212e-09 ----------------------------------------------------------------------------------------------------- 5 Ta 1 -5.308326064817097e-01 -5.308326064655580e-01 1.61517e-11 5.33450e-10 2 2.193364745336530e+00 2.193364745026588e+00 3.09942e-10 3.80861e-09 3 2.052835718165597e+00 2.052835718257811e+00 9.22138e-11 1.37898e-09 ----------------------------------------------------------------------------------------------------- 6 Ta 1 -1.573622374370701e+00 -1.573622374610272e+00 2.39572e-10 5.99604e-09 2 -5.304076048757759e-01 -5.304076049921815e-01 1.16406e-10 1.62340e-09 3 1.659518161026900e+00 1.659518161312712e+00 2.85812e-10 3.51000e-09 ----------------------------------------------------------------------------------------------------- 7 Ta 1 -1.063732869198948e+00 -1.063732869185984e+00 1.29639e-11 1.49977e-09 2 1.892957007983285e+00 1.892957007594828e+00 3.88457e-10 8.36540e-10 3 -1.936720802040686e-01 -1.936720802412445e-01 3.71760e-11 1.51781e-09 ----------------------------------------------------------------------------------------------------- 8 Ta 1 7.848466470829895e-01 7.848466445493077e-01 2.53368e-09 1.39922e-08 2 -2.623178045093955e+00 -2.623178045036096e+00 5.78595e-11 2.72061e-09 3 2.827165041590399e-01 2.827165044247337e-01 2.65694e-10 1.62746e-09 ----------------------------------------------------------------------------------------------------- 9 Ta 1 1.227301407779362e+00 1.227301407041658e+00 7.37704e-10 2.71785e-09 2 -4.923281086249441e-01 -4.923281085188633e-01 1.06081e-10 2.41159e-09 3 1.521144219388179e+00 1.521144219550675e+00 1.62496e-10 1.64435e-09 ----------------------------------------------------------------------------------------------------- 10 Ta 1 8.707429517704919e-02 8.707429507333828e-02 1.03711e-10 6.30295e-09 2 -7.909666408680607e-01 -7.909666394669617e-01 1.40110e-09 4.00308e-09 3 1.549888962259424e+00 1.549888962218988e+00 4.04368e-11 5.76934e-09 ----------------------------------------------------------------------------------------------------- 11 Ta 1 -4.972387995967953e-01 -4.972387998337490e-01 2.36954e-10 9.84986e-09 2 1.124240783115082e+00 1.124240783013148e+00 1.01934e-10 3.21461e-10 3 -9.850328163143326e-01 -9.850328163523175e-01 3.79849e-11 1.00826e-08 ----------------------------------------------------------------------------------------------------- 12 Ta 1 1.343169482892065e+00 1.343169482920158e+00 2.80929e-11 8.48027e-10 2 -7.677747526844229e-01 -7.677747527624613e-01 7.80385e-11 1.96940e-09 3 -2.878405591588406e-01 -2.878405607600406e-01 1.60120e-09 5.08044e-09 ----------------------------------------------------------------------------------------------------- 13 Ta 1 5.714558674232366e-01 5.714558519599791e-01 1.54633e-08 3.82290e-08 2 5.867006636903769e-01 5.867006593715109e-01 4.31887e-09 4.02358e-08 3 3.171260924058000e-01 3.171260921628068e-01 2.42993e-10 4.73676e-09 ----------------------------------------------------------------------------------------------------- 14 Ta 1 -2.184948490344469e+00 -2.184948481764282e+00 8.58019e-09 5.76808e-08 2 -1.847911621432154e+00 -1.847911621381635e+00 5.05198e-11 4.44909e-08 3 2.026493719777666e+00 2.026493719984745e+00 2.07079e-10 1.22498e-09 ----------------------------------------------------------------------------------------------------- 15 Ta 1 -2.200490608059349e-01 -2.200490608375255e-01 3.15906e-11 6.80068e-09 2 1.755964068005484e+00 1.755964067046140e+00 9.59344e-10 1.73986e-07 * 3 -9.026358113252068e-01 -9.026358113633186e-01 3.81118e-11 1.49964e-09 ----------------------------------------------------------------------------------------------------- 16 Ta 1 -2.545293753600487e-02 -2.545294013445995e-02 2.59846e-09 8.69456e-09 2 -1.352404130474900e+00 -1.352404128772618e+00 1.70228e-09 1.54960e-08 3 -3.891866719017222e-01 -3.891866719700819e-01 6.83597e-11 1.07937e-08 ----------------------------------------------------------------------------------------------------- 17 Ta 1 1.536109577713575e+00 1.536109577339309e+00 3.74267e-10 9.22747e-09 2 9.985264929612897e-01 9.985264929225143e-01 3.87754e-11 3.39094e-10 3 1.123006653409284e+00 1.123006653453627e+00 4.43439e-11 1.70289e-09 ----------------------------------------------------------------------------------------------------- 18 Ta 1 -3.431273515337956e+00 -3.431273513013828e+00 2.32413e-09 4.60032e-08 2 -1.800945845158851e+00 -1.800945840492993e+00 4.66586e-09 1.79657e-08 3 -2.738653049532203e+00 -2.738653048761154e+00 7.71049e-10 1.97402e-08 ----------------------------------------------------------------------------------------------------- 19 Ta 1 -2.544774191177401e+00 -2.544774191101912e+00 7.54889e-11 6.13060e-09 2 -1.814229349850224e+00 -1.814229349894573e+00 4.43485e-11 2.41395e-09 3 -3.614356319379431e-01 -3.614356317943305e-01 1.43613e-10 1.21775e-09 ----------------------------------------------------------------------------------------------------- 20 Ta 1 1.888010348239242e+00 1.888010348716175e+00 4.76934e-10 2.95382e-09 2 1.885989046365665e-01 1.885989056462095e-01 1.00964e-09 4.62351e-09 3 -2.007829462379296e+00 -2.007829461890203e+00 4.89094e-10 6.41922e-09 ----------------------------------------------------------------------------------------------------- 21 Ta 1 1.985339703929462e-02 1.985339481816198e-02 2.22113e-09 8.18523e-08 * 2 1.145393627702760e+00 1.145393635234453e+00 7.53169e-09 2.93026e-07 * 3 -5.259009294331706e-01 -5.259009201192059e-01 9.31396e-09 8.76463e-09 ----------------------------------------------------------------------------------------------------- 22 Ta 1 -8.001173062434194e-01 -8.001173060136851e-01 2.29734e-10 2.52245e-09 2 -1.910226320461923e+00 -1.910226320542265e+00 8.03424e-11 6.13189e-09 3 -5.351315640665509e-01 -5.351315640938209e-01 2.72700e-11 4.05464e-09 ----------------------------------------------------------------------------------------------------- 23 Ta 1 -1.157895302420549e+00 -1.157895303256529e+00 8.35981e-10 2.03492e-08 2 1.683187730187930e+00 1.683187729355616e+00 8.32314e-10 9.16014e-08 * 3 -1.686604376189876e+00 -1.686604373837927e+00 2.35195e-09 2.58581e-07 * ----------------------------------------------------------------------------------------------------- 24 Ta 1 4.487992248714424e+00 4.487992248617629e+00 9.67955e-11 2.89069e-09 2 1.749106507353423e+00 1.749106507610123e+00 2.56700e-10 1.24228e-08 3 2.016685868537782e+00 2.016685868119899e+00 4.17882e-10 2.43050e-09 ----------------------------------------------------------------------------------------------------- 25 Ta 1 -5.958263703177618e-03 -5.958263370874960e-03 3.32303e-10 5.20957e-09 2 3.025685893703696e-01 3.025685895137150e-01 1.43345e-10 3.62002e-09 3 4.209055370434957e-01 4.209055368796109e-01 1.63885e-10 2.83290e-09 ----------------------------------------------------------------------------------------------------- 26 Ta 1 -1.142202997034793e-01 -1.142203062975171e-01 6.59404e-09 8.31670e-08 * 2 -1.360985708574858e+00 -1.360985708721337e+00 1.46480e-10 9.28317e-09 3 3.340002796961858e-01 3.340002747787246e-01 4.91746e-09 8.86704e-08 * ----------------------------------------------------------------------------------------------------- 27 Ta 1 -9.236960970178666e-01 -9.236960969566553e-01 6.12113e-11 1.90284e-09 2 -6.806550157703448e-01 -6.806550147315082e-01 1.03884e-09 2.14859e-09 3 4.572046750711256e-01 4.572046758829228e-01 8.11797e-10 3.68281e-10 ----------------------------------------------------------------------------------------------------- 28 Ta 1 2.102608195216729e+00 2.102608191900348e+00 3.31638e-09 5.41577e-08 2 -9.767629482111084e-01 -9.767629491852704e-01 9.74162e-10 5.57018e-09 3 -1.529419319129041e+00 -1.529419315689611e+00 3.43943e-09 2.14400e-07 * ----------------------------------------------------------------------------------------------------- 29 Ta 1 1.874428311343252e+00 1.874428316799010e+00 5.45576e-09 1.62225e-08 2 2.463271052520425e+00 2.463270988139543e+00 6.43809e-08 2.38370e-07 * 3 -4.837370133930203e-01 -4.837370138765790e-01 4.83559e-10 3.22304e-08 ----------------------------------------------------------------------------------------------------- 30 Ta 1 -2.037868024470280e+00 -2.037868023988359e+00 4.81920e-10 7.11278e-09 2 -2.440292842775475e+00 -2.440292843144588e+00 3.69113e-10 9.24338e-09 3 4.139655414158977e-01 4.139655416037810e-01 1.87883e-10 1.15215e-08 ----------------------------------------------------------------------------------------------------- 31 Ta 1 -1.328933577811402e+00 -1.328933559803746e+00 1.80077e-08 4.16197e-08 2 6.806777673218559e-01 6.806777703487791e-01 3.02692e-09 8.58422e-09 3 -6.430183583859096e-01 -6.430183584054754e-01 1.95658e-11 2.82388e-08 ----------------------------------------------------------------------------------------------------- 32 Ta 1 -1.625433602535485e-01 -1.625433597001587e-01 5.53390e-10 1.07355e-08 2 -7.598897609046924e-01 -7.598897610174973e-01 1.12805e-10 5.91260e-10 3 -1.871236538477249e+00 -1.871236538064445e+00 4.12803e-10 3.91354e-09 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 16, direction = 1: |F_model - F_numer| error = ----------------------- = 1.02089e-07 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 = Cu Ta | a0 = 3.70267880853 | (Configuration in file "config-CuTa.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ta 1 1.684535695237101e+00 1.684535693107954e+00 2.12915e-09 2.61732e-08 2 -1.084941297796342e+00 -1.084941297904484e+00 1.08142e-10 1.02135e-08 3 -2.100710657024231e+00 -2.100710657681523e+00 6.57292e-10 1.27175e-08 ----------------------------------------------------------------------------------------------------- 2 Cu 1 9.372826595480818e-01 9.372826606833120e-01 1.13523e-09 8.46593e-09 2 -4.265125112821798e+00 -4.265125114063264e+00 1.24147e-09 6.13616e-09 3 -2.703973396355849e+00 -2.703973395805896e+00 5.49953e-10 2.92854e-08 ----------------------------------------------------------------------------------------------------- 3 Cu 1 -3.535198775719858e+00 -3.535198774437721e+00 1.28214e-09 1.34259e-08 2 -8.786775553122843e-01 -8.786775542351495e-01 1.07713e-09 1.21272e-08 3 -3.411332739447936e+00 -3.411332737753833e+00 1.69410e-09 7.70521e-09 ----------------------------------------------------------------------------------------------------- 4 Ta 1 -2.958112366449386e+00 -2.958112366014810e+00 4.34576e-10 1.57394e-09 2 4.540198668991123e+00 4.540198669723179e+00 7.32056e-10 2.88408e-09 3 -2.986156991971090e+00 -2.986156992290135e+00 3.19045e-10 3.11301e-09 ----------------------------------------------------------------------------------------------------- 5 Ta 1 -2.692739805708460e-02 -2.692739840080449e-02 3.43720e-10 6.68867e-09 2 1.686260398089988e+00 1.686260397633958e+00 4.56030e-10 1.02980e-07 3 1.218125641138832e+00 1.218125643305458e+00 2.16663e-09 5.74554e-09 ----------------------------------------------------------------------------------------------------- 6 Ta 1 7.906166416768647e-02 7.906166418339261e-02 1.57061e-11 2.20086e-09 2 -4.350798251613457e+00 -4.350798251505421e+00 1.08036e-10 3.12290e-09 3 -3.063632609744071e+00 -3.063632609721211e+00 2.28599e-11 1.35605e-09 ----------------------------------------------------------------------------------------------------- 7 Cu 1 -2.854007015386278e-01 -2.854007026497893e-01 1.11116e-09 6.53701e-09 2 -4.437882927099562e-02 -4.437882788476540e-02 1.38623e-09 2.31055e-08 3 -4.573439094670189e-01 -4.573439088102696e-01 6.56749e-10 1.65077e-08 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -2.608350695262843e-01 -2.608350695447840e-01 1.84997e-11 1.37506e-08 2 -5.001164269843835e-01 -5.001164276596921e-01 6.75309e-10 1.08748e-08 3 -5.397722656269694e-01 -5.397722653670556e-01 2.59914e-10 6.12564e-09 ----------------------------------------------------------------------------------------------------- 9 Ta 1 -6.330052933494745e+00 -6.330052933494930e+00 1.84741e-13 1.10485e-08 2 -2.995378292123362e+00 -2.995378291604586e+00 5.18776e-10 7.28750e-10 3 -6.047064449277896e+00 -6.047064449433394e+00 1.55498e-10 1.95018e-06 * ----------------------------------------------------------------------------------------------------- 10 Cu 1 2.511462740399506e+00 2.511462740294166e+00 1.05340e-10 3.03496e-09 2 2.465483116291602e+00 2.465483116106311e+00 1.85291e-10 1.04166e-09 3 -2.165083519057971e+00 -2.165083519070774e+00 1.28026e-11 6.47554e-10 ----------------------------------------------------------------------------------------------------- 11 Ta 1 2.659032394811851e+00 2.659032382495522e+00 1.23163e-08 7.11513e-07 * 2 2.292199085641651e+00 2.292199039764918e+00 4.58767e-08 4.37431e-07 * 3 5.958754013818816e+00 5.958754024977889e+00 1.11591e-08 4.81442e-07 * ----------------------------------------------------------------------------------------------------- 12 Ta 1 -1.351686150814110e+00 -1.351686150728107e+00 8.60034e-11 6.57793e-10 2 1.176140636181752e+00 1.176140636904058e+00 7.22306e-10 1.67808e-10 3 4.013323363299611e+00 4.013323360900848e+00 2.39876e-09 1.38581e-08 ----------------------------------------------------------------------------------------------------- 13 Ta 1 -4.339719079942878e+00 -4.339719034176799e+00 4.57661e-08 1.21386e-07 * 2 -4.162026452793728e-01 -4.162026311359622e-01 1.41434e-08 6.34822e-08 3 -6.047686214830508e+00 -6.047686220536829e+00 5.70632e-09 1.12914e-07 * ----------------------------------------------------------------------------------------------------- 14 Cu 1 1.798708612541363e+00 1.798708612283156e+00 2.58207e-10 3.91977e-10 2 2.194419505273245e+00 2.194419505239529e+00 3.37157e-11 2.24056e-10 3 -5.811998648631178e-01 -5.811998647666295e-01 9.64883e-11 4.16730e-09 ----------------------------------------------------------------------------------------------------- 15 Ta 1 5.816541672750766e+00 5.816541674813445e+00 2.06268e-09 1.83935e-08 2 1.718149589388484e+00 1.718149575193846e+00 1.41946e-08 1.42497e-07 * 3 6.957632172889812e+00 6.957632173029253e+00 1.39441e-10 2.16786e-08 ----------------------------------------------------------------------------------------------------- 16 Ta 1 1.456774583726876e+00 1.456774583678278e+00 4.85987e-11 2.84895e-09 2 6.262763367735622e+00 6.262763367489455e+00 2.46167e-10 5.35988e-08 3 -3.350051443552577e+00 -3.350051444116162e+00 5.63586e-10 6.63651e-10 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -3.413282361785279e-01 -3.413282360747592e-01 1.03769e-10 2.15609e-07 * 2 -4.452080546702242e+00 -4.452080552368423e+00 5.66618e-09 2.09860e-08 3 2.125196955387165e+00 2.125196956483849e+00 1.09668e-09 1.79854e-08 ----------------------------------------------------------------------------------------------------- 18 Ta 1 4.948559241203292e+00 4.948559144339683e+00 9.68636e-08 2.35815e-07 * 2 -2.124662965790004e+00 -2.124662958589025e+00 7.20098e-09 2.61047e-07 * 3 4.636412578846361e+00 4.636412540890497e+00 3.79559e-08 2.92970e-07 * ----------------------------------------------------------------------------------------------------- 19 Ta 1 1.980178213732255e+00 1.980178213892227e+00 1.59972e-10 3.20152e-10 2 2.027500526766369e+00 2.027500525720327e+00 1.04604e-09 2.09758e-08 3 -1.090138579139476e+00 -1.090138578644985e+00 4.94492e-10 7.61208e-09 ----------------------------------------------------------------------------------------------------- 20 Cu 1 5.395304777395735e-02 5.395305102034666e-02 3.24639e-09 2.56551e-09 2 8.769018302165114e-01 8.769018304004944e-01 1.83983e-10 6.31810e-09 3 1.088201290112455e+00 1.088201290452863e+00 3.40409e-10 2.83951e-08 ----------------------------------------------------------------------------------------------------- 21 Ta 1 2.743161530526750e+00 2.743161531924659e+00 1.39791e-09 3.33787e-09 2 -2.539482240314031e+00 -2.539482236789123e+00 3.52491e-09 4.80574e-09 3 4.385858248622540e+00 4.385858248187989e+00 4.34551e-10 5.35354e-10 ----------------------------------------------------------------------------------------------------- 22 Ta 1 6.374935175622674e+00 6.374936135353768e+00 9.59731e-07 1.25105e-06 * 2 3.628784577458355e-01 3.628781319404528e-01 3.25805e-07 7.03182e-07 * 3 -5.494557624467361e+00 -5.494557555136152e+00 6.93312e-08 4.53892e-07 * ----------------------------------------------------------------------------------------------------- 23 Cu 1 -1.068436087757472e+00 -1.068436087576422e+00 1.81050e-10 7.27468e-09 2 5.174164634259087e-01 5.174164640032791e-01 5.77370e-10 2.04680e-08 3 -7.444047867593875e-01 -7.444047753966578e-01 1.13627e-08 2.62913e-08 ----------------------------------------------------------------------------------------------------- 24 Ta 1 -5.964153465890901e+00 -5.964153466036669e+00 1.45768e-10 9.47980e-09 2 -7.739567412322055e-01 -7.739567413963827e-01 1.64177e-10 1.25529e-08 3 6.061828936603444e+00 6.061828937178194e+00 5.74750e-10 2.87420e-08 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -2.587897952096746e+00 -2.587897954413725e+00 2.31698e-09 4.86199e-08 2 3.588182672427051e+00 3.588182670674336e+00 1.75271e-09 4.44112e-08 3 6.777655656343995e-01 6.777655623611647e-01 3.27323e-09 9.11044e-09 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -3.321789896639444e+00 -3.321789898651202e+00 2.01176e-09 6.18893e-09 2 8.118160005921679e-02 8.118159832256133e-02 1.73666e-09 8.77364e-09 3 1.919199742354736e+00 1.919199741249596e+00 1.10514e-09 2.26169e-08 ----------------------------------------------------------------------------------------------------- 27 Ta 1 -1.890333344171474e+00 -1.890333343726879e+00 4.44595e-10 1.96659e-09 2 -3.597013815502306e-01 -3.597013812982779e-01 2.51953e-10 3.61060e-09 3 -2.164230924049300e-01 -2.164230923799818e-01 2.49482e-11 1.85295e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 1.194367881014103e+00 1.194367881016834e+00 2.73070e-12 3.18050e-09 2 -9.882328243783759e-01 -9.882328231401527e-01 1.23822e-09 1.76829e-08 3 -1.087289149975629e+00 -1.087289152190491e+00 2.21486e-09 3.64632e-09 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -3.157119821949044e-01 -3.157119665298959e-01 1.56650e-08 6.24428e-08 2 -3.713083110649001e+00 -3.713083110200826e+00 4.48175e-10 3.05182e-08 3 3.654119483936476e+00 3.654119484025309e+00 8.88329e-11 2.88494e-08 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -3.164610463350455e-01 -3.164610460142381e-01 3.20807e-10 7.54848e-09 2 -5.068910337517274e-01 -5.068910337431759e-01 8.55149e-12 3.51074e-09 3 -6.348357427907606e-01 -6.348357435303773e-01 7.39617e-10 4.16803e-09 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -4.648981088008238e-01 -4.648981097267216e-01 9.25898e-10 1.51772e-08 2 -2.867863233725403e-01 -2.867863222581939e-01 1.11435e-09 3.06159e-08 3 -2.198885704757217e-01 -2.198885717556751e-01 1.27995e-09 9.56482e-08 ----------------------------------------------------------------------------------------------------- 32 Cu 1 1.120387482552046e+00 1.120387484271859e+00 1.71981e-09 8.82134e-09 2 4.908196607079895e-01 4.908196603123541e-01 3.95635e-10 1.98779e-09 3 2.451276145878495e-01 2.451276158884163e-01 1.30057e-09 3.58475e-08 ----------------------------------------------------------------------------------------------------- * 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 = 20, direction = 1: |F_model - F_numer| error = ----------------------- = 6.01706e-08 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.02089e-07 Machine precision = 2.22045e-16 Note: Lower grades can reflect errors in the analytical forces, a lack of smoothness in the potential, or loss of precision in the numerical derivative computation. Grade: B Comment: The letter grade B was assigned because the normalized error in the computation was 1.02089e-07 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.