!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : EMT_Asap_MetalGlass_PaduraruKenoufiBailey_2007_CuZr__MO_987541074959_000 Supported species : Cu Zr 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 = 3.58786964417 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 1.335862814787657e-02 1.335862814834257e-02 4.66001e-13 4.52942e-11 2 -1.675854142612391e+00 -1.675854142610787e+00 1.60361e-12 3.25762e-11 3 -1.837604179956999e+00 -1.837604179955421e+00 1.57807e-12 3.18285e-11 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -2.131275945637180e+00 -2.131275945643862e+00 6.68221e-12 9.21885e-12 2 2.072830509749115e+00 2.072830509700249e+00 4.88662e-11 1.28611e-10 3 3.562861498778735e-01 3.562861498794480e-01 1.57446e-12 6.33956e-11 ----------------------------------------------------------------------------------------------------- 3 Cu 1 1.042581646257585e+00 1.042581646278836e+00 2.12508e-11 2.52758e-11 2 -3.823794080123528e-01 -3.823794080102678e-01 2.08494e-12 1.01618e-10 3 -4.580069567111060e-01 -4.580069567198281e-01 8.72213e-12 4.54364e-11 ----------------------------------------------------------------------------------------------------- 4 Cu 1 2.897060302432122e-01 2.897060302438114e-01 5.99132e-13 2.96055e-11 2 2.272573483872975e+00 2.272573483854007e+00 1.89684e-11 9.36566e-11 3 1.914879094660898e+00 1.914879094664009e+00 3.11084e-12 1.61011e-11 ----------------------------------------------------------------------------------------------------- 5 Cu 1 1.555881306743506e+00 1.555881306753712e+00 1.02067e-11 3.54088e-11 2 -1.928738689957337e+00 -1.928738689951004e+00 6.33316e-12 2.49407e-11 3 5.758883206209910e-01 5.758883206192958e-01 1.69520e-12 1.70752e-11 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -1.810054983557359e-01 -1.810054983540782e-01 1.65767e-12 4.76434e-11 2 6.924846801919127e-01 6.924846801840907e-01 7.82197e-12 2.04461e-11 3 4.236311774916523e-01 4.236311774897545e-01 1.89782e-12 4.77575e-11 ----------------------------------------------------------------------------------------------------- 7 Cu 1 5.752101147415244e-01 5.752101147495272e-01 8.00282e-12 4.74936e-11 2 -3.151303095651177e+00 -3.151303095657775e+00 6.59872e-12 5.80398e-11 3 -3.611239412406596e+00 -3.611239412397132e+00 9.46354e-12 6.51821e-11 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -1.192638991028080e+00 -1.192638991037733e+00 9.65317e-12 2.09845e-11 2 -5.584691386816084e-01 -5.584691386806326e-01 9.75775e-13 1.43526e-09 * 3 -8.065308916288593e-01 -8.065308916278903e-01 9.69003e-13 2.67918e-11 ----------------------------------------------------------------------------------------------------- 9 Cu 1 -8.951389674284471e-02 -8.951389675765942e-02 1.48147e-11 1.78849e-11 2 -3.975832201534663e-01 -3.975832201545657e-01 1.09940e-12 1.18071e-11 3 -3.020189199870800e-01 -3.020189199825319e-01 4.54808e-12 8.32941e-11 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -1.118174736115469e+00 -1.118174736116041e+00 5.71321e-13 8.62665e-12 2 9.500356392988029e-01 9.500356393150020e-01 1.61992e-11 4.45438e-11 3 -1.433047971341830e+00 -1.433047971343587e+00 1.75682e-12 7.26534e-11 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -1.095297480657399e+00 -1.095297480654843e+00 2.55551e-12 3.63154e-11 2 -1.515854150281835e+00 -1.515854150254738e+00 2.70972e-11 9.50817e-12 3 1.713905795768534e+00 1.713905795777478e+00 8.94396e-12 1.73497e-11 ----------------------------------------------------------------------------------------------------- 12 Cu 1 3.476263349308353e-01 3.476263349291518e-01 1.68349e-12 6.04469e-11 2 4.914797496077675e-01 4.914797496058076e-01 1.95988e-12 6.93262e-12 3 -2.969031043454877e-01 -2.969031043388617e-01 6.62598e-12 2.69168e-12 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -1.998795261849483e+00 -1.998795261842063e+00 7.42006e-12 3.11304e-11 2 -3.368934262932954e+00 -3.368934262938059e+00 5.10436e-12 2.17875e-11 3 -4.241435243920346e+00 -4.241435243918193e+00 2.15294e-12 4.95586e-11 ----------------------------------------------------------------------------------------------------- 14 Cu 1 1.254512872725853e+00 1.254512872725028e+00 8.25340e-13 1.13352e-11 2 2.551723902757575e+00 2.551723902754079e+00 3.49587e-12 1.79043e-11 3 -1.534792668268838e+00 -1.534792668279593e+00 1.07550e-11 4.23108e-11 ----------------------------------------------------------------------------------------------------- 15 Cu 1 3.618583082028658e+00 3.618583082033885e+00 5.22649e-12 5.95808e-11 2 -4.225738509520802e+00 -4.225738509517180e+00 3.62199e-12 3.66001e-11 3 5.503234170665128e-01 5.503234170666110e-01 9.82547e-14 8.92051e-11 ----------------------------------------------------------------------------------------------------- 16 Cu 1 -2.354404621889728e-01 -2.354404621948585e-01 5.88576e-12 5.40038e-10 * 2 3.358804773063682e+00 3.358804773065584e+00 1.90203e-12 6.03628e-11 3 1.963579082479773e+00 1.963579082470169e+00 9.60454e-12 4.43496e-11 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -4.126659975765416e-01 -4.126659975792432e-01 2.70162e-12 5.29038e-12 2 -2.675970776854357e-01 -2.675970776896860e-01 4.25032e-12 5.69781e-11 3 -5.411453268874453e-01 -5.411453268891654e-01 1.72007e-12 1.73020e-11 ----------------------------------------------------------------------------------------------------- 18 Cu 1 4.994019758463759e-01 4.994019758464874e-01 1.11466e-13 2.20811e-11 2 1.144735617278010e+00 1.144735617297072e+00 1.90616e-11 2.63962e-11 3 7.046175237250423e-01 7.046175237263547e-01 1.31239e-12 1.58774e-11 ----------------------------------------------------------------------------------------------------- 19 Cu 1 1.167069025397161e+00 1.167069025396890e+00 2.70672e-13 6.68947e-11 2 -4.483274096640704e-01 -4.483274096687258e-01 4.65544e-12 3.46541e-11 3 -1.910444944549176e-01 -1.910444944549735e-01 5.58165e-14 4.88948e-11 ----------------------------------------------------------------------------------------------------- 20 Cu 1 -3.313884860353479e-01 -3.313884860352316e-01 1.16240e-13 1.01666e-10 2 1.408096711219678e+00 1.408096711223416e+00 3.73723e-12 3.50522e-11 3 7.975027332947410e-02 7.975027332789740e-02 1.57670e-12 6.80113e-11 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.637683370526923e+00 -1.637683370546420e+00 1.94971e-11 1.09881e-11 2 -1.797951392690077e-01 -1.797951392651347e-01 3.87304e-12 1.79286e-11 3 1.056158736874454e+00 1.056158736875457e+00 1.00275e-12 2.41806e-10 * ----------------------------------------------------------------------------------------------------- 22 Cu 1 1.053171599830332e+00 1.053171599842484e+00 1.21514e-11 2.79454e-11 2 3.243171747948507e+00 3.243171747951924e+00 3.41682e-12 7.64064e-11 3 3.057766419945201e+00 3.057766419944577e+00 6.24389e-13 4.52856e-11 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -4.157543584465544e-01 -4.157543584415786e-01 4.97580e-12 7.16582e-11 2 3.626290308441128e-01 3.626290308425726e-01 1.54016e-12 8.47777e-11 3 -3.693148418738005e-01 -3.693148418738466e-01 4.60743e-14 2.56793e-11 ----------------------------------------------------------------------------------------------------- 24 Cu 1 3.241658500001313e-02 3.241658500042416e-02 4.11025e-13 5.10707e-12 2 4.176344040517924e-01 4.176344040539886e-01 2.19619e-12 1.55889e-10 3 -7.062522570087026e-01 -7.062522569958758e-01 1.28269e-11 1.70058e-10 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -3.273620587896358e-01 -3.273620587869412e-01 2.69457e-12 6.30067e-11 2 -1.405360246551579e+00 -1.405360246541746e+00 9.83325e-12 1.62925e-11 3 -7.971765399807479e-02 -7.971765399556184e-02 2.51295e-12 6.28570e-11 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -8.062300889549274e-01 -8.062300889620204e-01 7.09299e-12 2.45403e-11 2 1.148542686506779e+00 1.148542686507525e+00 7.46070e-13 1.21434e-10 3 -1.174114044505673e+00 -1.174114044508737e+00 3.06377e-12 7.77689e-12 ----------------------------------------------------------------------------------------------------- 27 Cu 1 1.802328809687018e+00 1.802328809685960e+00 1.05871e-12 1.68976e-11 2 -3.849310204014887e+00 -3.849310204022360e+00 7.47269e-12 2.32934e-10 * 3 7.159130070190159e-01 7.159130070241644e-01 5.14844e-12 5.27034e-11 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -2.164114450453880e+00 -2.164114450426343e+00 2.75375e-11 6.59157e-11 2 2.213429438718082e+00 2.213429438716704e+00 1.37801e-12 1.91314e-11 3 2.823839940869094e-02 2.823839941396143e-02 5.27049e-12 4.20529e-12 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -1.838968223321283e+00 -1.838968223320138e+00 1.14442e-12 4.09424e-11 2 -1.317516336450180e+00 -1.317516336449652e+00 5.28022e-13 6.95761e-11 3 4.100050692677875e-01 4.100050692650436e-01 2.74386e-12 5.48044e-10 * ----------------------------------------------------------------------------------------------------- 30 Cu 1 6.028077674805823e-01 6.028077674794259e-01 1.15641e-12 2.92302e-11 2 2.961908211793142e+00 2.961908211797941e+00 4.79883e-12 6.18825e-11 3 1.782901220468679e+00 1.782901220460678e+00 8.00116e-12 6.13853e-11 ----------------------------------------------------------------------------------------------------- 31 Cu 1 1.217821660035286e+00 1.217821660037422e+00 2.13563e-12 2.02645e-11 2 -1.457270231205861e+00 -1.457270231203708e+00 2.15294e-12 2.15330e-11 3 1.662216309981239e+00 1.662216309979711e+00 1.52811e-12 1.89870e-11 ----------------------------------------------------------------------------------------------------- 32 Cu 1 9.038318675844388e-01 9.038318675721347e-01 1.23040e-11 1.93969e-11 2 8.399506757430144e-01 8.399506757401898e-01 2.82463e-12 2.36476e-11 3 5.871079693099381e-01 5.871079693140606e-01 4.12248e-12 2.09401e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 28, direction = 3: |F_model - F_numer| error = ----------------------- = 1.86643e-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 = Zr | a0 = 4.55288028717 | (Configuration in file "config-Zr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 1.151553380900340e+00 1.151553380894546e+00 5.79403e-12 4.01534e-11 2 1.193722506011973e+00 1.193722506001549e+00 1.04243e-11 1.01186e-11 3 1.130654715897506e+00 1.130654715875661e+00 2.18447e-11 2.92846e-11 ----------------------------------------------------------------------------------------------------- 2 Zr 1 1.691051584152551e-01 1.691051584360719e-01 2.08168e-11 1.00701e-10 2 -3.229510107272868e-01 -3.229510107257816e-01 1.50513e-12 1.62421e-11 3 -2.076244247663394e-01 -2.076244247763677e-01 1.00283e-11 5.86724e-11 ----------------------------------------------------------------------------------------------------- 3 Zr 1 -3.481925459059558e-01 -3.481925459056767e-01 2.79055e-13 3.26698e-11 2 -8.706955468202047e-01 -8.706955468160719e-01 4.13281e-12 7.97507e-12 3 -4.506185023861296e-01 -4.506185023915744e-01 5.44481e-12 7.49843e-11 ----------------------------------------------------------------------------------------------------- 4 Zr 1 -2.150196395800719e-01 -2.150196395600643e-01 2.00075e-11 1.04669e-10 2 -8.369512604491072e-02 -8.369512602550819e-02 1.94025e-11 3.16767e-11 3 8.220926821468577e-02 8.220926821669416e-02 2.00839e-12 5.66968e-10 * ----------------------------------------------------------------------------------------------------- 5 Zr 1 3.170070441794660e-01 3.170070441851046e-01 5.63866e-12 1.78133e-11 2 1.063805181615203e+00 1.063805181622365e+00 7.16294e-12 2.20624e-11 3 1.138573878476649e+00 1.138573878473030e+00 3.61888e-12 1.16849e-11 ----------------------------------------------------------------------------------------------------- 6 Zr 1 -1.124443112117689e+00 -1.124443112120156e+00 2.46692e-12 1.17415e-11 2 -2.238789034602249e-01 -2.238789034619348e-01 1.70983e-12 2.92541e-11 3 9.790602038417866e-01 9.790602038394270e-01 2.35956e-12 3.46707e-11 ----------------------------------------------------------------------------------------------------- 7 Zr 1 -4.417927758562419e-01 -4.417927758524536e-01 3.78830e-12 1.25459e-11 2 7.307573781653043e-01 7.307573781654315e-01 1.27232e-13 6.10073e-11 3 -6.262458469933577e-01 -6.262458469947205e-01 1.36280e-12 2.74401e-11 ----------------------------------------------------------------------------------------------------- 8 Zr 1 1.026273894360160e+00 1.026273894361111e+00 9.50351e-13 1.42086e-11 2 -4.105871639185684e-02 -4.105871637207330e-02 1.97835e-11 2.36579e-11 3 -6.608237366584343e-01 -6.608237366469383e-01 1.14960e-11 3.87448e-09 * ----------------------------------------------------------------------------------------------------- 9 Zr 1 3.540007072064018e-01 3.540007072115580e-01 5.15621e-12 2.97017e-11 2 -6.048421647846891e-01 -6.048421647784192e-01 6.26987e-12 2.55874e-11 3 -5.787036295453405e-01 -5.787036295431419e-01 2.19857e-12 3.22251e-11 ----------------------------------------------------------------------------------------------------- 10 Zr 1 2.694132226760336e-01 2.694132226786997e-01 2.66603e-12 4.93707e-11 2 -8.244782911072446e-01 -8.244782911163745e-01 9.12992e-12 2.87979e-11 3 7.410630170242971e-01 7.410630170238343e-01 4.62852e-13 3.55687e-11 ----------------------------------------------------------------------------------------------------- 11 Zr 1 -7.895661638220111e-01 -7.895661638394236e-01 1.74125e-11 6.05554e-10 * 2 6.878818302571096e-01 6.878818302555367e-01 1.57285e-12 6.30440e-12 3 -1.356073832457731e+00 -1.356073832386232e+00 7.14995e-11 6.63577e-10 * ----------------------------------------------------------------------------------------------------- 12 Zr 1 3.917617732270330e-01 3.917617732305841e-01 3.55105e-12 8.11831e-11 2 5.852301469465834e-01 5.852301469428003e-01 3.78308e-12 3.63046e-11 3 6.323971208561826e-01 6.323971208445885e-01 1.15941e-11 2.20751e-11 ----------------------------------------------------------------------------------------------------- 13 Zr 1 4.414473582144640e-01 4.414473582132720e-01 1.19199e-12 6.54252e-11 2 7.455616859736293e-01 7.455616859693234e-01 4.30589e-12 2.75842e-11 3 9.673124112875910e-01 9.673124112926648e-01 5.07372e-12 4.39475e-11 ----------------------------------------------------------------------------------------------------- 14 Zr 1 -1.529628479379162e+00 -1.529628479377539e+00 1.62292e-12 1.51148e-11 2 -1.221327384755301e+00 -1.221327384758629e+00 3.32867e-12 6.95666e-12 3 1.290135348603510e+00 1.290135348600244e+00 3.26517e-12 3.77391e-11 ----------------------------------------------------------------------------------------------------- 15 Zr 1 -1.010500984200514e+00 -1.010500984204899e+00 4.38516e-12 4.47042e-11 2 3.465772263767204e-01 3.465772263895761e-01 1.28557e-11 3.77765e-10 * 3 -3.459048201484204e-01 -3.459048201394341e-01 8.98626e-12 4.63620e-11 ----------------------------------------------------------------------------------------------------- 16 Zr 1 6.677648192847375e-01 6.677648192733440e-01 1.13936e-11 1.68904e-11 2 -9.637690124916702e-01 -9.637690125071963e-01 1.55260e-11 5.08676e-11 3 -3.221254149376414e-01 -3.221254149191553e-01 1.84860e-11 4.06088e-11 ----------------------------------------------------------------------------------------------------- 17 Zr 1 7.772668382988245e-01 7.772668383068858e-01 8.06133e-12 4.89289e-11 2 6.572154142241959e-01 6.572154142273751e-01 3.17912e-12 1.09167e-11 3 5.010991518151661e-01 5.010991518119912e-01 3.17490e-12 2.15488e-11 ----------------------------------------------------------------------------------------------------- 18 Zr 1 -9.475582078165979e-01 -9.475582078230324e-01 6.43441e-12 1.19258e-10 2 -1.406864477369586e+00 -1.406864477351081e+00 1.85052e-11 2.68860e-11 3 3.317175482797134e-01 3.317175482729001e-01 6.81333e-12 5.62681e-10 * ----------------------------------------------------------------------------------------------------- 19 Zr 1 -4.135345858202287e-01 -4.135345858224809e-01 2.25220e-12 2.91167e-12 2 1.003572652711903e+00 1.003572652713422e+00 1.51834e-12 1.64004e-11 3 -1.058826160270603e+00 -1.058826160269604e+00 9.98535e-13 7.06413e-12 ----------------------------------------------------------------------------------------------------- 20 Zr 1 6.134583286595260e-01 6.134583286588839e-01 6.42042e-13 2.05646e-11 2 -3.320080869182346e-01 -3.320080869161376e-01 2.09699e-12 2.44876e-11 3 -4.642058582317827e-01 -4.642058582312042e-01 5.78426e-13 3.22186e-11 ----------------------------------------------------------------------------------------------------- 21 Zr 1 -2.240458282618346e-01 -2.240458282661685e-01 4.33389e-12 7.65299e-11 2 2.150710541243596e-01 2.150710541479308e-01 2.35711e-11 1.90967e-10 * 3 5.457164195997768e-01 5.457164196033661e-01 3.58935e-12 5.44652e-11 ----------------------------------------------------------------------------------------------------- 22 Zr 1 1.659117026045727e-01 1.659117026061831e-01 1.61043e-12 2.39761e-11 2 1.626478488834843e-01 1.626478488998989e-01 1.64145e-11 5.17853e-11 3 1.792035116693381e-01 1.792035116680441e-01 1.29396e-12 6.58427e-11 ----------------------------------------------------------------------------------------------------- 23 Zr 1 -8.411400063516316e-01 -8.411400063482756e-01 3.35598e-12 1.86733e-11 2 9.477756074539226e-01 9.477756074678394e-01 1.39168e-11 2.64726e-11 3 -1.067121881341780e+00 -1.067121881343601e+00 1.82054e-12 3.36233e-11 ----------------------------------------------------------------------------------------------------- 24 Zr 1 4.187561942218255e-01 4.187561942082926e-01 1.35328e-11 2.57730e-11 2 -3.252805471584366e-01 -3.252805471666486e-01 8.21204e-12 9.34530e-12 3 1.393174568677182e-01 1.393174568663511e-01 1.36710e-12 3.50581e-11 ----------------------------------------------------------------------------------------------------- 25 Zr 1 4.054233925523483e-02 4.054233925993547e-02 4.70064e-12 4.44385e-11 2 2.110487200558462e-01 2.110487200680039e-01 1.21577e-11 2.87075e-11 3 3.865756714864864e-01 3.865756714916951e-01 5.20867e-12 2.64164e-11 ----------------------------------------------------------------------------------------------------- 26 Zr 1 1.120874650224417e-01 1.120874650189756e-01 3.46606e-12 1.46995e-10 2 -2.833056861077466e-01 -2.833056861216268e-01 1.38802e-11 3.82788e-11 3 5.287430292916433e-01 5.287430292936476e-01 2.00429e-12 9.43261e-11 ----------------------------------------------------------------------------------------------------- 27 Zr 1 -1.720839812289040e-01 -1.720839812273452e-01 1.55878e-12 5.82022e-11 2 5.186848603322756e-01 5.186848603391779e-01 6.90237e-12 3.84293e-11 3 -2.837399314753009e-01 -2.837399314787537e-01 3.45279e-12 1.97835e-11 ----------------------------------------------------------------------------------------------------- 28 Zr 1 1.057872500424973e+00 1.057872500417425e+00 7.54841e-12 5.16645e-11 2 -1.067943142442918e+00 -1.067943142448079e+00 5.16120e-12 1.29101e-11 3 -1.058011059089836e+00 -1.058011059089222e+00 6.13731e-13 9.11873e-11 ----------------------------------------------------------------------------------------------------- 29 Zr 1 2.023638151797957e+00 2.023638151796960e+00 9.96980e-13 8.89715e-11 2 1.459928923175584e+00 1.459928923166134e+00 9.45000e-12 1.54435e-10 3 7.794327697973937e-01 7.794327697904319e-01 6.96188e-12 6.16263e-11 ----------------------------------------------------------------------------------------------------- 30 Zr 1 -1.176494526067053e+00 -1.176494526067566e+00 5.12923e-13 4.66958e-11 2 -1.121851454474696e+00 -1.121851454501792e+00 2.70963e-11 2.30784e-10 * 3 3.278921158553588e-01 3.278921158514811e-01 3.87773e-12 3.38337e-11 ----------------------------------------------------------------------------------------------------- 31 Zr 1 -1.486589676533483e+00 -1.486589676514197e+00 1.92859e-11 4.55323e-10 * 2 4.696579223348762e-01 4.696579223279606e-01 6.91569e-12 4.09660e-11 3 -1.000586626127373e+00 -1.000586626127572e+00 1.99618e-13 1.15914e-10 ----------------------------------------------------------------------------------------------------- 32 Zr 1 7.227296341921311e-01 7.227296341980871e-01 5.95601e-12 3.78924e-11 2 -1.305189407587963e+00 -1.305189407587070e+00 8.93730e-13 1.15610e-11 3 -1.200491914434733e+00 -1.200491914432795e+00 1.93823e-12 2.79332e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 8, direction = 2: |F_model - F_numer| error = ----------------------- = 4.81835e-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 = Cu Zr | a0 = 3.92407024538 | (Configuration in file "config-CuZr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 1.026627134144051e+00 1.026627134143102e+00 9.48575e-13 1.27408e-10 2 8.944167967038720e-01 8.944167967014424e-01 2.42961e-12 2.49202e-11 3 7.088141411641019e-01 7.088141411708910e-01 6.78912e-12 1.20688e-10 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -1.547124499096936e+00 -1.547124499103472e+00 6.53655e-12 2.19085e-11 2 8.941100352545860e-02 8.941100352694985e-02 1.49125e-12 1.45785e-11 3 -2.388441853800116e-01 -2.388441853324188e-01 4.75928e-11 8.11750e-11 ----------------------------------------------------------------------------------------------------- 3 Zr 1 -3.314437001404194e+00 -3.314437001416854e+00 1.26605e-11 2.90172e-11 2 -1.519759934021985e+00 -1.519759934025659e+00 3.67373e-12 5.28091e-11 3 -4.037868282415896e+00 -4.037868282415142e+00 7.54063e-13 1.95763e-11 ----------------------------------------------------------------------------------------------------- 4 Cu 1 -1.128221475417722e+00 -1.128221475437151e+00 1.94289e-11 1.86017e-10 2 -4.842541295208301e-01 -4.842541295232435e-01 2.41335e-12 1.23037e-10 3 -1.769070485090207e+00 -1.769070485090338e+00 1.31228e-13 4.97880e-11 ----------------------------------------------------------------------------------------------------- 5 Cu 1 -3.196366000191004e-01 -3.196366000211541e-01 2.05369e-12 7.43017e-12 2 -8.198441321334703e-01 -8.198441321397740e-01 6.30374e-12 5.87981e-11 3 2.649622291347057e-01 2.649622291409477e-01 6.24201e-12 3.79853e-11 ----------------------------------------------------------------------------------------------------- 6 Zr 1 3.515937943055650e+00 3.515937943049979e+00 5.67058e-12 2.88538e-11 2 -4.074077888209287e+00 -4.074077888219319e+00 1.00320e-11 3.30536e-11 3 -2.744704444841569e+00 -2.744704444834110e+00 7.45892e-12 5.36637e-11 ----------------------------------------------------------------------------------------------------- 7 Zr 1 1.139620264772155e+00 1.139620264746061e+00 2.60945e-11 3.07834e-11 2 -1.712473620783147e+00 -1.712473620783577e+00 4.29656e-13 1.89740e-10 3 -1.238449485510411e+00 -1.238449485509922e+00 4.88942e-13 5.16163e-11 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -1.460514767912745e+00 -1.460514767910295e+00 2.44937e-12 4.84819e-11 2 -8.606957610715649e-01 -8.606957610743949e-01 2.83007e-12 1.00248e-11 3 -1.589483745257279e+00 -1.589483745290072e+00 3.27931e-11 3.14304e-11 ----------------------------------------------------------------------------------------------------- 9 Zr 1 6.733948712851671e-01 6.733948712776023e-01 7.56473e-12 7.97509e-11 2 2.926255289559652e-01 2.926255289547180e-01 1.24722e-12 4.24363e-11 3 9.449024154793954e-01 9.449024154887002e-01 9.30489e-12 6.43476e-11 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -1.368199970253764e-01 -1.368199970304350e-01 5.05854e-12 4.55089e-12 2 -3.210195881920851e-01 -3.210195881918496e-01 2.35534e-13 4.65630e-11 3 2.001789539053984e-01 2.001789538775560e-01 2.78424e-11 2.85355e-11 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -6.534633534398013e-02 -6.534633535163645e-02 7.65632e-12 4.68095e-11 2 -1.009739217889539e+00 -1.009739217890357e+00 8.17568e-13 3.14697e-11 3 -1.454688203780726e+00 -1.454688203780114e+00 6.11955e-13 5.92786e-11 ----------------------------------------------------------------------------------------------------- 12 Cu 1 7.750864352350341e-01 7.750864352998302e-01 6.47962e-11 1.10463e-09 * 2 -9.701136362642075e-01 -9.701136362630436e-01 1.16396e-12 6.35059e-11 3 -1.564367875790116e-01 -1.564367875579504e-01 2.10612e-11 1.96703e-10 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -3.101932154407777e+00 -3.101932154407704e+00 7.37188e-14 5.90417e-12 2 4.393163119553146e+00 4.393163119548298e+00 4.84768e-12 8.27773e-11 3 -1.275898403612009e-01 -1.275898403677946e-01 6.59361e-12 7.00176e-11 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -5.880527636889491e-01 -5.880527636643407e-01 2.46084e-11 7.74821e-11 2 -5.715066440635798e-01 -5.715066440605132e-01 3.06655e-12 4.78546e-11 3 5.636526991429960e-01 5.636526991452964e-01 2.30038e-12 5.62871e-11 ----------------------------------------------------------------------------------------------------- 15 Zr 1 1.603970824876999e+00 1.603970824867906e+00 9.09317e-12 2.15179e-11 2 2.404972195339507e+00 2.404972195340562e+00 1.05516e-12 1.88159e-10 3 1.589051025744684e+00 1.589051025744626e+00 5.86198e-14 7.17114e-10 * ----------------------------------------------------------------------------------------------------- 16 Cu 1 4.842352988385764e-01 4.842352988356406e-01 2.93571e-12 3.77981e-12 2 -4.200952999053496e-01 -4.200952999151103e-01 9.76075e-12 5.60196e-12 3 -8.142013064572154e-01 -8.142013064428221e-01 1.43934e-11 1.71918e-10 ----------------------------------------------------------------------------------------------------- 17 Cu 1 7.949822607313290e-01 7.949822607335227e-01 2.19369e-12 3.42614e-11 2 5.292752827284156e-01 5.292752827222630e-01 6.15263e-12 4.60711e-11 3 -1.614835613556879e-01 -1.614835613619890e-01 6.30104e-12 5.49213e-12 ----------------------------------------------------------------------------------------------------- 18 Zr 1 2.176619257342861e+00 2.176619257363448e+00 2.05862e-11 4.32809e-11 2 -1.911475512080672e+00 -1.911475512081736e+00 1.06337e-12 3.74676e-11 3 2.781148675948477e-01 2.781148675796754e-01 1.51723e-11 4.11377e-11 ----------------------------------------------------------------------------------------------------- 19 Cu 1 -8.738794013275575e-01 -8.738794013285854e-01 1.02796e-12 5.94181e-11 2 3.698311802915252e-01 3.698311802754809e-01 1.60443e-11 2.35183e-10 * 3 6.045270776099372e-01 6.045270776137605e-01 3.82328e-12 4.53655e-11 ----------------------------------------------------------------------------------------------------- 20 Zr 1 -1.300585772063555e+00 -1.300585772044693e+00 1.88622e-11 1.40758e-10 2 -1.165981958834690e+00 -1.165981958828548e+00 6.14220e-12 2.65525e-11 3 2.078098011486357e+00 2.078098011487608e+00 1.25100e-12 4.98384e-11 ----------------------------------------------------------------------------------------------------- 21 Zr 1 3.234950354893015e+00 3.234950354896613e+00 3.59757e-12 1.11798e-10 2 -1.058176316960853e+00 -1.058176316962484e+00 1.63136e-12 1.36804e-11 3 3.526413938601273e+00 3.526413938604322e+00 3.04956e-12 8.58780e-11 ----------------------------------------------------------------------------------------------------- 22 Cu 1 7.626776183978249e-01 7.626776183920325e-01 5.79237e-12 8.21450e-11 2 7.359006963967719e-01 7.359006963841997e-01 1.25722e-11 7.38767e-11 3 2.493060605105899e+00 2.493060605106259e+00 3.60156e-13 7.54135e-11 ----------------------------------------------------------------------------------------------------- 23 Zr 1 -1.123183924445970e+00 -1.123183924470124e+00 2.41549e-11 7.50526e-10 * 2 1.116704891407023e+00 1.116704891411831e+00 4.80771e-12 7.37741e-11 3 -1.104527403614185e+00 -1.104527403614331e+00 1.45883e-13 1.79976e-11 ----------------------------------------------------------------------------------------------------- 24 Cu 1 4.564723962954273e-01 4.564723962983175e-01 2.89024e-12 3.10167e-11 2 -1.142420854394943e-01 -1.142420854518041e-01 1.23098e-11 2.42673e-11 3 -6.765414043803681e-01 -6.765414043829702e-01 2.60203e-12 6.14931e-11 ----------------------------------------------------------------------------------------------------- 25 Zr 1 -3.751220483795310e+00 -3.751220483773159e+00 2.21512e-11 1.84998e-09 * 2 1.738025206872091e+00 1.738025206871434e+00 6.57252e-13 1.20819e-11 3 -7.186717744750065e-01 -7.186717744787073e-01 3.70082e-12 7.45363e-11 ----------------------------------------------------------------------------------------------------- 26 Zr 1 -2.482040887622287e+00 -2.482040887624491e+00 2.20446e-12 6.38711e-11 2 4.038169111988918e+00 4.038169111994543e+00 5.62572e-12 1.41641e-10 3 -6.136289519607456e-01 -6.136289519594246e-01 1.32105e-12 6.41815e-11 ----------------------------------------------------------------------------------------------------- 27 Cu 1 3.670354411664148e-01 3.670354411621884e-01 4.22640e-12 4.38451e-11 2 5.343582170508320e-01 5.343582170492527e-01 1.57929e-12 1.06165e-11 3 1.485065252397524e+00 1.485065252395555e+00 1.96865e-12 2.34097e-10 * ----------------------------------------------------------------------------------------------------- 28 Cu 1 5.614928075655587e-01 5.614928075768099e-01 1.12511e-11 3.10730e-11 2 -7.843858911911937e-02 -7.843858911724576e-02 1.87361e-12 3.58266e-11 3 -7.845648188950831e-02 -7.845648187359248e-02 1.59158e-11 5.24141e-11 ----------------------------------------------------------------------------------------------------- 29 Zr 1 2.634451192664017e+00 2.634451192667801e+00 3.78364e-12 7.20006e-11 2 -8.836384557600271e-01 -8.836384557579527e-01 2.07434e-12 1.45356e-10 3 1.100768452621446e+00 1.100768452617288e+00 4.15823e-12 2.48921e-11 ----------------------------------------------------------------------------------------------------- 30 Zr 1 1.282754076131433e+00 1.282754076124257e+00 7.17604e-12 1.29878e-11 2 5.921154964579884e-01 5.921154964490646e-01 8.92386e-12 2.38165e-11 3 -4.049309570455355e-01 -4.049309570506397e-01 5.10419e-12 3.84859e-12 ----------------------------------------------------------------------------------------------------- 31 Zr 1 -8.338062879088094e-01 -8.338062879250433e-01 1.62339e-11 2.50436e-11 2 -3.641452907942477e-01 -3.641452907881362e-01 6.11144e-12 1.03090e-10 3 -7.068397303533194e-01 -7.068397303437114e-01 9.60798e-12 4.85280e-11 ----------------------------------------------------------------------------------------------------- 32 Zr 1 5.364941740847553e-01 5.364941740833606e-01 1.39466e-12 5.53004e-11 2 6.107093337726385e-01 6.107093337734042e-01 7.65721e-13 2.92169e-11 3 2.798807361759319e+00 2.798807361757062e+00 2.25775e-12 1.24687e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as dicontinuities. Maximum error obtained for particle = 28, direction = 3: |F_model - F_numer| error = ----------------------- = 2.02862e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.81835e-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 4.81835e-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.