!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : MEAM_LAMMPS_JeongParkDo_2018_PdTi__MO_086900950763_002 Supported species : Pd Ti 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 = Pd | a0 = 3.889087677001953 | (Configuration in file "config-Pd.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pd 1 4.461756305709966e-01 4.461756305265756e-01 4.44210e-11 9.52156e-11 2 -3.065855761789613e-01 -3.065855762513220e-01 7.23607e-11 5.79757e-11 3 -3.438369847001623e-01 -3.438369847070705e-01 6.90820e-12 1.20928e-10 ----------------------------------------------------------------------------------------------------- 2 Pd 1 -1.921795827249019e-01 -1.921795827513162e-01 2.64143e-11 4.44533e-10 2 7.111047907620169e-01 7.111047907992277e-01 3.72108e-11 8.85149e-11 3 3.550720151148114e-02 3.550720152174643e-02 1.02653e-11 4.41188e-10 ----------------------------------------------------------------------------------------------------- 3 Pd 1 1.205360016987321e+00 1.205360016922843e+00 6.44775e-11 2.01100e-10 2 -5.436820889643076e-01 -5.436820889986903e-01 3.43827e-11 1.06717e-10 3 4.550002020827175e-01 4.550002020970190e-01 1.43014e-11 4.55765e-10 ----------------------------------------------------------------------------------------------------- 4 Pd 1 2.102014859865139e-01 2.102014859840773e-01 2.43658e-12 1.71082e-10 2 1.153824886357926e+00 1.153824886348781e+00 9.14557e-12 1.37638e-10 3 6.975295049529279e-01 6.975295049313480e-01 2.15798e-11 2.65646e-10 ----------------------------------------------------------------------------------------------------- 5 Pd 1 -1.060404471161045e-01 -1.060404472188687e-01 1.02764e-10 1.68362e-10 2 3.504107085357334e-01 3.504107084414078e-01 9.43256e-11 1.74834e-10 3 4.879914054861027e-01 4.879914055176494e-01 3.15467e-11 1.36665e-10 ----------------------------------------------------------------------------------------------------- 6 Pd 1 -9.709534706665104e-02 -9.709534703452710e-02 3.21239e-11 1.82150e-10 2 5.121666111448766e-01 5.121666111338261e-01 1.10505e-11 1.37846e-11 3 5.255581213290961e-01 5.255581213241410e-01 4.95504e-12 1.13592e-11 ----------------------------------------------------------------------------------------------------- 7 Pd 1 -5.060432985499036e-01 -5.060432985258553e-01 2.40483e-11 4.43495e-10 2 -3.541482008967264e+00 -3.541482008945014e+00 2.22498e-11 1.33623e-10 3 -3.866447133583737e+00 -3.866447133521129e+00 6.26086e-11 4.98313e-10 ----------------------------------------------------------------------------------------------------- 8 Pd 1 -1.957848625819353e+00 -1.957848625791368e+00 2.79847e-11 2.76168e-10 2 -2.694121119966916e+00 -2.694121119917946e+00 4.89706e-11 2.38462e-10 3 -9.896682959349850e-01 -9.896682959774372e-01 4.24523e-11 4.43484e-10 ----------------------------------------------------------------------------------------------------- 9 Pd 1 2.932293100073680e-01 2.932293100428234e-01 3.54555e-11 8.32579e-11 2 -1.312120817126624e+00 -1.312120817118679e+00 7.94542e-12 4.93448e-11 3 -6.725236788778152e-01 -6.725236788893642e-01 1.15490e-11 1.17136e-08 * ----------------------------------------------------------------------------------------------------- 10 Pd 1 -1.049945862452693e+00 -1.049945862454436e+00 1.74349e-12 1.97905e-10 2 4.643730865725963e-01 4.643730865451531e-01 2.74433e-11 1.48599e-10 3 -1.148049066277497e+00 -1.148049066266491e+00 1.10056e-11 2.35913e-10 ----------------------------------------------------------------------------------------------------- 11 Pd 1 -6.340274934672254e-01 -6.340274935157088e-01 4.84833e-11 1.34584e-10 2 -9.825907827408011e-01 -9.825907827283339e-01 1.24672e-11 4.18898e-10 3 -3.564574879167162e-01 -3.564574879238805e-01 7.16438e-12 9.25698e-11 ----------------------------------------------------------------------------------------------------- 12 Pd 1 -4.045936397704377e-01 -4.045936397695886e-01 8.49154e-13 5.42039e-11 2 1.170887979750142e+00 1.170887979756879e+00 6.73706e-12 1.84724e-10 3 3.718857160318894e-01 3.718857160140561e-01 1.78333e-11 1.44085e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 -2.126185639296313e+00 -2.126185639296985e+00 6.71907e-13 4.22173e-10 2 -2.110715109741362e+00 -2.110715109769496e+00 2.81344e-11 1.24978e-09 3 -4.244037658196052e+00 -4.244037658243711e+00 4.76588e-11 1.02802e-10 ----------------------------------------------------------------------------------------------------- 14 Pd 1 -2.410403298828414e-01 -2.410403298762560e-01 6.58537e-12 8.75248e-11 2 8.996241983218516e-01 8.996241983063917e-01 1.54599e-11 1.84966e-10 3 2.812723956554464e-01 2.812723956620513e-01 6.60483e-12 1.82792e-10 ----------------------------------------------------------------------------------------------------- 15 Pd 1 4.697038442054041e+00 4.697038442080003e+00 2.59615e-11 7.70788e-11 2 -2.694285294160924e+00 -2.694285294152408e+00 8.51674e-12 2.86930e-10 3 1.163275754459025e+00 1.163275754452732e+00 6.29274e-12 1.22684e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 8.284787781134051e-01 8.284787780654118e-01 4.79933e-11 8.11264e-10 2 3.128350681518711e+00 3.128350681595195e+00 7.64846e-11 4.05178e-10 3 8.983753106290081e-01 8.983753106474464e-01 1.84383e-11 2.69851e-10 ----------------------------------------------------------------------------------------------------- 17 Pd 1 -4.061454098686907e-01 -4.061454098928812e-01 2.41905e-11 6.77451e-11 2 -5.012973939769411e-01 -5.012973939556820e-01 2.12591e-11 7.16560e-10 3 -9.846937219540294e-01 -9.846937219588882e-01 4.85878e-12 1.36741e-10 ----------------------------------------------------------------------------------------------------- 18 Pd 1 6.886334401180052e-01 6.886334401689124e-01 5.09072e-11 8.01861e-10 2 1.717980257880749e+00 1.717980257940056e+00 5.93072e-11 6.65699e-11 3 3.758367885060694e-01 3.758367884787188e-01 2.73506e-11 4.54978e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 1.187025105388809e+00 1.187025105388369e+00 4.40092e-13 2.51023e-10 2 -7.673650622451951e-01 -7.673650622456279e-01 4.32876e-13 8.99778e-10 3 8.898253417270421e-02 8.898253423659960e-02 6.38954e-11 1.14424e-09 ----------------------------------------------------------------------------------------------------- 20 Pd 1 -6.439149472052798e-01 -6.439149472075628e-01 2.28306e-12 1.02867e-11 2 1.644804666684211e+00 1.644804666682559e+00 1.65157e-12 6.02693e-09 * 3 4.139079614686256e-01 4.139079614682112e-01 4.14335e-13 3.19020e-10 ----------------------------------------------------------------------------------------------------- 21 Pd 1 -7.509464459917160e-01 -7.509464459881339e-01 3.58213e-12 8.00829e-10 2 1.914155628111527e-01 1.914155628165997e-01 5.44700e-12 1.10914e-09 3 -7.665970663038410e-02 -7.665970663551512e-02 5.13102e-12 4.68682e-11 ----------------------------------------------------------------------------------------------------- 22 Pd 1 6.918346538239658e-01 6.918346538499746e-01 2.60088e-11 7.90922e-10 2 4.784037018678341e+00 4.784037018560885e+00 1.17456e-10 4.08287e-10 3 4.082974530434764e+00 4.082974530487233e+00 5.24691e-11 4.17893e-10 ----------------------------------------------------------------------------------------------------- 23 Pd 1 -6.178851032984695e-01 -6.178851032966622e-01 1.80722e-12 1.26732e-10 2 4.545779294766472e-01 4.545779294776672e-01 1.02002e-12 4.39893e-10 3 -5.076687120422380e-01 -5.076687120214909e-01 2.07471e-11 6.92814e-11 ----------------------------------------------------------------------------------------------------- 24 Pd 1 1.433003135961311e-01 1.433003136045050e-01 8.37391e-12 1.46775e-10 2 2.473658363711074e-01 2.473658363747527e-01 3.64528e-12 4.11807e-11 3 -9.575779752795094e-01 -9.575779752727247e-01 6.78468e-12 8.75289e-11 ----------------------------------------------------------------------------------------------------- 25 Pd 1 -5.620482469743164e-01 -5.620482470389049e-01 6.45884e-11 2.95372e-10 2 -9.335156363513351e-01 -9.335156363768938e-01 2.55588e-11 3.32993e-10 3 8.576839208957038e-01 8.576839208758420e-01 1.98618e-11 2.86836e-09 * ----------------------------------------------------------------------------------------------------- 26 Pd 1 -1.184233684801010e+00 -1.184233684793857e+00 7.15294e-12 2.29495e-10 2 1.389424273050106e+00 1.389424273097529e+00 4.74227e-11 9.08439e-10 3 -3.780764888169298e-01 -3.780764888363441e-01 1.94144e-11 6.20621e-10 ----------------------------------------------------------------------------------------------------- 27 Pd 1 2.467645072943484e+00 2.467645072904647e+00 3.88369e-11 1.03838e-10 2 -4.791687686438070e+00 -4.791687686459648e+00 2.15774e-11 1.36044e-10 3 6.649095815219408e-01 6.649095815397013e-01 1.77605e-11 5.91959e-10 ----------------------------------------------------------------------------------------------------- 28 Pd 1 -2.212639158915868e+00 -2.212639158907703e+00 8.16547e-12 4.73799e-11 2 2.598813001944294e+00 2.598813001977576e+00 3.32814e-11 2.58692e-10 3 -7.341920376956671e-01 -7.341920376836331e-01 1.20340e-11 2.06924e-10 ----------------------------------------------------------------------------------------------------- 29 Pd 1 -4.499725912533619e-01 -4.499725912611042e-01 7.74231e-12 2.45607e-10 2 -1.415211941771008e+00 -1.415211941823864e+00 5.28559e-11 4.42879e-10 3 2.311021405312257e+00 2.311021405371124e+00 5.88667e-11 2.32218e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 3.030399963353254e-01 3.030399963384108e-01 3.08542e-12 1.71444e-10 2 1.042446000901669e+00 1.042446000842405e+00 5.92633e-11 3.11871e-10 3 1.360850514421800e+00 1.360850514438006e+00 1.62057e-11 2.24394e-10 ----------------------------------------------------------------------------------------------------- 31 Pd 1 1.724519878738359e-01 1.724519878804810e-01 6.64510e-12 4.89061e-10 2 -7.012037448793080e-01 -7.012037449698399e-01 9.05319e-11 5.67636e-11 3 -4.107141071075447e-01 -4.107141071084163e-01 8.71636e-13 3.17640e-11 ----------------------------------------------------------------------------------------------------- 32 Pd 1 8.083716206559334e-01 8.083716206976931e-01 4.17597e-11 2.49314e-10 2 8.342567727468881e-01 8.342567727573850e-01 1.04968e-11 2.66769e-10 3 5.980402061417077e-01 5.980402061352659e-01 6.44185e-12 5.64485e-10 ----------------------------------------------------------------------------------------------------- * 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 = 5, direction = 1: |F_model - F_numer| error = ----------------------- = 9.69104e-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 = Ti | a0 = 4.133002281188965 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 3.451553151832584e-01 3.451553151804836e-01 2.77472e-12 1.09100e-10 2 1.546196741987336e-01 1.546196742026588e-01 3.92525e-12 3.31664e-11 3 3.800418312763711e-01 3.800418312766991e-01 3.28015e-13 3.45519e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -2.106481257950507e-01 -2.106481257874955e-01 7.55518e-12 1.06766e-10 2 -5.768116837357336e-02 -5.768116837378277e-02 2.09416e-13 1.91862e-11 3 1.062157277747283e+00 1.062157277725244e+00 2.20388e-11 1.18076e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 3.344690059664885e-01 3.344690059507832e-01 1.57053e-11 1.29262e-10 2 6.288512427687096e-01 6.288512427415656e-01 2.71441e-11 1.55689e-10 3 -5.583148689980935e-01 -5.583148690034835e-01 5.39002e-12 3.98964e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -4.022191063877909e-01 -4.022191063833360e-01 4.45494e-12 1.59091e-09 * 2 -1.873226499180193e+00 -1.873226499187000e+00 6.80767e-12 1.87428e-11 3 1.023358057652998e+00 1.023358057665751e+00 1.27534e-11 3.66468e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -5.881775399345706e-01 -5.881775399201455e-01 1.44250e-11 9.45327e-11 2 -8.642133087708059e-02 -8.642133086102355e-02 1.60570e-11 1.20941e-10 3 -8.949473563768970e-01 -8.949473563679422e-01 8.95484e-12 1.09567e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 5.579844112885826e-01 5.579844113022571e-01 1.36745e-11 1.20328e-10 2 -5.025482159390191e-01 -5.025482159526778e-01 1.36587e-11 9.81376e-11 3 -3.141499455952840e-02 -3.141499456935682e-02 9.82842e-12 2.87022e-09 * ----------------------------------------------------------------------------------------------------- 7 Ti 1 2.126670655198589e+00 2.126670655202165e+00 3.57536e-12 2.58731e-11 2 -1.247375179823397e+00 -1.247375179830085e+00 6.68865e-12 2.96818e-11 3 2.741496719554125e-01 2.741496719529035e-01 2.50905e-12 7.30620e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -1.653329412656381e+00 -1.653329412679904e+00 2.35230e-11 1.96717e-09 * 2 2.359808326171845e+00 2.359808326180140e+00 8.29470e-12 2.03375e-10 3 -5.923199261181634e-01 -5.923199261079138e-01 1.02496e-11 1.38036e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -4.185848310273349e-01 -4.185848310272744e-01 6.05072e-14 3.91762e-10 2 1.199436516628576e+00 1.199436516588134e+00 4.04414e-11 1.44755e-10 3 -5.875340519371368e-01 -5.875340519322377e-01 4.89908e-12 2.94095e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 8.451146124189479e-01 8.451146124293516e-01 1.04037e-11 1.29158e-10 2 -7.087799075012309e-01 -7.087799075228175e-01 2.15866e-11 1.83435e-10 3 -3.544873099665957e-01 -3.544873099805657e-01 1.39700e-11 1.80521e-09 * ----------------------------------------------------------------------------------------------------- 11 Ti 1 -1.280387218859235e+00 -1.280387218839981e+00 1.92533e-11 1.50832e-09 * 2 8.987640680147547e-01 8.987640680263235e-01 1.15687e-11 4.44651e-11 3 -2.553312380784639e+00 -2.553312380935506e+00 1.50868e-10 1.95418e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -1.741880513435197e-01 -1.741880513301491e-01 1.33706e-11 7.14435e-11 2 -4.181731871229200e-01 -4.181731870643454e-01 5.85746e-11 8.09088e-11 3 1.005710117157746e+00 1.005710117173312e+00 1.55669e-11 7.98690e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -3.150048201590778e-01 -3.150048201292886e-01 2.97892e-11 7.33686e-11 2 -1.330028822197078e+00 -1.330028822135119e+00 6.19587e-11 2.61048e-10 3 -1.810134838024231e-01 -1.810134838925026e-01 9.00795e-11 1.39493e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 8.649194611166808e-01 8.649194610952821e-01 2.13988e-11 3.58735e-09 * 2 5.044949781765059e-01 5.044949781893626e-01 1.28567e-11 1.20761e-10 3 -1.491096841763551e-01 -1.491096841782214e-01 1.86626e-12 4.45773e-11 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -4.269937528079841e-01 -4.269937528160607e-01 8.07654e-12 6.27881e-11 2 5.821535766638227e-01 5.821535765933458e-01 7.04770e-11 1.77863e-10 3 -7.772816028532491e-01 -7.772816028497597e-01 3.48943e-12 2.42930e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.984291968146902e-01 -1.984291968374029e-01 2.27127e-11 1.38483e-09 * 2 8.456326649517756e-01 8.456326649309619e-01 2.08137e-11 1.83239e-10 3 8.427329791410468e-01 8.427329791472051e-01 6.15830e-12 2.62404e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 5.203043413193907e-01 5.203043412727320e-01 4.66588e-11 2.21308e-10 2 3.258403825011406e-01 3.258403824850044e-01 1.61362e-11 3.80418e-11 3 1.316852477586735e-01 1.316852477548303e-01 3.84323e-12 4.52871e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -1.106602916488875e+00 -1.106602916455380e+00 3.34945e-11 2.06661e-11 2 -3.076010758516267e+00 -3.076010758321166e+00 1.95101e-10 1.26324e-10 3 -1.937423072160965e+00 -1.937423072100765e+00 6.02003e-11 2.89472e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -7.868730976318123e-01 -7.868730975670342e-01 6.47782e-11 1.19662e-10 2 -7.873588845937294e-01 -7.873588846013945e-01 7.66509e-12 7.88438e-11 3 1.331785769077335e-01 1.331785768154953e-01 9.22383e-11 2.65875e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -6.423122662877450e-01 -6.423122662749688e-01 1.27761e-11 2.94048e-10 2 -1.036484695951653e+00 -1.036484695992165e+00 4.05118e-11 9.84843e-11 3 8.420170243000480e-01 8.420170242458196e-01 5.42284e-11 6.43345e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 -4.927875732066326e-01 -4.927875732392943e-01 3.26617e-11 1.90850e-10 2 4.967563674306605e-01 4.967563674807832e-01 5.01227e-11 1.55758e-10 3 9.176039938519600e-01 9.176039938637147e-01 1.17547e-11 3.78264e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -8.424360871701171e-01 -8.424360872126794e-01 4.25623e-11 1.46395e-09 * 2 -8.075377514514299e-01 -8.075377513846808e-01 6.67492e-11 2.89013e-10 3 8.437995952559473e-01 8.437995952782557e-01 2.23084e-11 4.86561e-11 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -3.327000460660524e-01 -3.327000460802428e-01 1.41904e-11 1.42530e-10 2 3.530219103418351e-01 3.530219103334400e-01 8.39501e-12 2.59628e-10 3 -2.820643620520800e-01 -2.820643620589931e-01 6.91308e-12 2.44321e-11 ----------------------------------------------------------------------------------------------------- 24 Ti 1 2.556570865389715e+00 2.556570865409628e+00 1.99125e-11 3.32021e-10 2 1.972088762700168e-01 1.972088762723883e-01 2.37144e-12 8.91374e-11 3 4.023209539592778e-01 4.023209539698959e-01 1.06181e-11 1.05172e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -7.980476478263869e-01 -7.980476478630045e-01 3.66176e-11 2.38011e-10 2 1.533096816643520e+00 1.533096816651236e+00 7.71583e-12 1.08527e-10 3 -7.286095384306355e-01 -7.286095384107265e-01 1.99090e-11 7.41935e-11 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -7.589555329493183e-01 -7.589555329576170e-01 8.29870e-12 5.34716e-11 2 1.244638076822871e+00 1.244638076905414e+00 8.25429e-11 2.57492e-10 3 -8.842745012070279e-01 -8.842745011524533e-01 5.45746e-11 9.41115e-11 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -7.675890425133597e-01 -7.675890424389203e-01 7.44393e-11 4.08036e-10 2 4.284655472903648e-01 4.284655472798053e-01 1.05594e-11 1.19749e-09 * 3 2.053733998484312e+00 2.053733998393064e+00 9.12483e-11 1.95306e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 3.456968347702066e-01 3.456968347744329e-01 4.22623e-12 1.33521e-10 2 -3.972266660454764e-01 -3.972266660433683e-01 2.10804e-12 4.30037e-11 3 -7.021573000925964e-01 -7.021573000990458e-01 6.44940e-12 4.26768e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 3.134653663241799e+00 3.134653663273419e+00 3.16196e-11 3.18296e-09 * 2 1.207800692379011e-01 1.207800692338614e-01 4.03974e-12 7.23945e-11 3 7.073032317986027e-01 7.073032318665978e-01 6.79952e-11 4.46441e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -2.931959662960718e-02 -2.931959664065886e-02 1.10517e-11 2.57775e-10 2 2.096459682392864e-01 2.096459682531803e-01 1.38939e-11 7.23647e-11 3 5.885225796203619e-01 5.885225796059649e-01 1.43970e-11 5.71904e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 1.572071028271698e-01 1.572071028887972e-01 6.16274e-11 3.39046e-10 2 -3.355528542060427e-01 -3.355528542103254e-01 4.28269e-12 8.36714e-10 3 -3.836236241111651e-01 -3.836236241405730e-01 2.94079e-11 1.14383e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 4.368395938347114e-01 4.368395938636126e-01 2.89012e-11 1.58383e-11 2 5.811908594267704e-01 5.811908594087829e-01 1.79875e-11 1.27645e-09 * 3 3.895729207597775e-01 3.895729207736616e-01 1.38841e-11 2.98370e-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 discontinuities. Maximum error obtained for particle = 19, direction = 3: |F_model - F_numer| error = ----------------------- = 6.92591e-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 = Pd Ti | a0 = 3.962873085374122 | (Configuration in file "config-PdTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Pd 1 -3.168167019204288e-02 -3.168167018906790e-02 2.97497e-12 1.02826e-11 2 -1.008351687059506e+00 -1.008351687077464e+00 1.79572e-11 3.59830e-11 3 -1.073572558463306e+00 -1.073572558463414e+00 1.07248e-13 1.81069e-10 ----------------------------------------------------------------------------------------------------- 2 Pd 1 1.692655108144503e+00 1.692655108147203e+00 2.69917e-12 1.54858e-10 2 -2.017819917761137e+00 -2.017819917698297e+00 6.28400e-11 5.00413e-10 3 -1.126338993693921e+00 -1.126338993707457e+00 1.35352e-11 1.98251e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -2.183092537806762e+00 -2.183092537809167e+00 2.40474e-12 1.77240e-10 2 -3.312966046858146e-02 -3.312966047924418e-02 1.06627e-11 4.63815e-11 3 5.513756433806632e-01 5.513756433564699e-01 2.41933e-11 3.97903e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.357185080451433e+00 -1.357185080512038e+00 6.06051e-11 8.62292e-11 2 1.202467384424962e+00 1.202467384481226e+00 5.62643e-11 4.46354e-11 3 1.600063165674216e+00 1.600063165659123e+00 1.50930e-11 8.05850e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 1.572215723676643e+00 1.572215723671217e+00 5.42610e-12 3.73230e-11 2 2.867205520411780e-01 2.867205520582781e-01 1.71001e-11 1.03207e-10 3 -1.374765158944937e+00 -1.374765158943739e+00 1.19815e-12 7.51210e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -4.668677149555021e-01 -4.668677149581845e-01 2.68241e-12 9.55991e-11 2 1.757796621493708e-01 1.757796621475691e-01 1.80170e-12 2.73525e-10 3 3.765599250140551e-01 3.765599250576636e-01 4.36086e-11 8.00283e-11 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -1.590550275955201e-01 -1.590550275995647e-01 4.04465e-12 1.05941e-10 2 -5.342192206435015e-01 -5.342192206517086e-01 8.20710e-12 9.22373e-11 3 -3.103366818646440e-01 -3.103366818644728e-01 1.71141e-13 1.67361e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.043586410657960e+00 1.043586410695168e+00 3.72076e-11 9.25882e-11 2 -1.327434408536152e+00 -1.327434408491248e+00 4.49039e-11 1.98219e-10 3 -3.075432613808301e+00 -3.075432613758542e+00 4.97584e-11 6.85816e-11 ----------------------------------------------------------------------------------------------------- 9 Pd 1 -1.104080326352690e+00 -1.104080326352736e+00 4.66294e-14 1.48804e-10 2 5.520133356249084e-01 5.520133355628470e-01 6.20614e-11 2.59847e-10 3 2.742001398556543e-01 2.742001398800317e-01 2.43774e-11 9.68110e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 5.407014074208286e-01 5.407014074157057e-01 5.12290e-12 6.68892e-11 2 -2.527771796570920e-01 -2.527771796627535e-01 5.66147e-12 3.17599e-09 * 3 4.509648018585469e-01 4.509648018410793e-01 1.74676e-11 4.02604e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 2.412643720129721e-01 2.412643719998381e-01 1.31340e-11 5.01316e-11 2 3.603173092830051e+00 3.603173092821110e+00 8.94040e-12 8.86690e-10 3 4.495875345585843e-02 4.495875340389836e-02 5.19601e-11 7.52092e-10 ----------------------------------------------------------------------------------------------------- 12 Pd 1 -8.119628674297654e-01 -8.119628674533430e-01 2.35776e-11 1.17257e-10 2 -6.131951406528667e-01 -6.131951406378172e-01 1.50495e-11 2.69329e-11 3 -1.144606972992512e+00 -1.144606972996308e+00 3.79519e-12 8.53226e-11 ----------------------------------------------------------------------------------------------------- 13 Pd 1 -9.457114906986264e-02 -9.457114906804691e-02 1.81573e-12 1.71083e-10 2 5.917372350130714e-01 5.917372350153787e-01 2.30727e-12 9.88250e-09 * 3 8.822291047791303e-01 8.822291048087664e-01 2.96361e-11 1.87000e-11 ----------------------------------------------------------------------------------------------------- 14 Pd 1 -6.075618863471794e-01 -6.075618863449137e-01 2.26574e-12 1.38695e-10 2 -4.539024886465922e-01 -4.539024886501335e-01 3.54128e-12 3.97963e-11 3 5.057116346791066e-01 5.057116346848263e-01 5.71965e-12 1.94875e-10 ----------------------------------------------------------------------------------------------------- 15 Pd 1 3.698990388507461e+00 3.698990388495241e+00 1.22204e-11 2.37300e-10 2 -2.155035836373107e+00 -2.155035836388210e+00 1.51030e-11 4.95896e-10 3 -2.934615359702239e+00 -2.934615359686479e+00 1.57603e-11 1.26244e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -2.467537311785853e+00 -2.467537311809561e+00 2.37081e-11 1.50533e-10 2 2.709896974291002e+00 2.709896974250666e+00 4.03357e-11 4.08782e-10 3 -2.242876258893003e+00 -2.242876258882514e+00 1.04889e-11 4.85998e-11 ----------------------------------------------------------------------------------------------------- 17 Pd 1 5.193750875952033e-01 5.193750876015895e-01 6.38611e-12 1.58209e-10 2 7.712461840990464e-02 7.712461851681228e-02 1.06908e-10 2.18814e-10 3 4.176008530290519e-01 4.176008530957528e-01 6.67009e-11 6.10024e-10 ----------------------------------------------------------------------------------------------------- 18 Pd 1 -1.161384622435615e+00 -1.161384622648968e+00 2.13353e-10 1.68563e-08 * 2 -1.530144474835305e+00 -1.530144474804505e+00 3.07996e-11 1.14215e-09 * 3 1.513395231418782e+00 1.513395231367222e+00 5.15603e-11 2.10998e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 1.542183226850585e+00 1.542183226839239e+00 1.13454e-11 6.86411e-11 2 -1.007521180134163e+00 -1.007521179991794e+00 1.42369e-10 5.93078e-10 3 -4.868495303178539e-01 -4.868495302900422e-01 2.78117e-11 1.33444e-10 ----------------------------------------------------------------------------------------------------- 20 Pd 1 -8.712194175616579e-01 -8.712194175431955e-01 1.84623e-11 5.79710e-11 2 1.655582069545493e+00 1.655582069436275e+00 1.09219e-10 8.44305e-11 3 -4.516252519112273e-01 -4.516252519488779e-01 3.76505e-11 4.13856e-09 * ----------------------------------------------------------------------------------------------------- 21 Ti 1 1.389578550997197e+00 1.389578550930092e+00 6.71043e-11 1.35401e-10 2 9.675817516168413e-01 9.675817515746189e-01 4.22224e-11 1.31691e-09 * 3 1.797502558869994e+00 1.797502558896909e+00 2.69151e-11 1.67030e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -2.986596307825544e-01 -2.986596307609244e-01 2.16299e-11 2.47146e-10 2 3.869403034219076e-01 3.869403034549478e-01 3.30402e-11 2.65144e-10 3 7.334133869275216e-01 7.334133869508124e-01 2.32908e-11 1.06926e-10 ----------------------------------------------------------------------------------------------------- 23 Pd 1 -5.360558395261692e-01 -5.360558395605630e-01 3.43938e-11 1.26156e-10 2 6.338229145173764e-01 6.338229145350277e-01 1.76513e-11 1.26033e-09 * 3 -6.510023263148673e-01 -6.510023263158276e-01 9.60232e-13 2.10751e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -9.878444470285782e-01 -9.878444470064648e-01 2.21134e-11 2.40201e-11 2 -1.668414571277526e+00 -1.668414571321658e+00 4.41316e-11 2.81341e-10 3 1.155133555058426e+00 1.155133555067127e+00 8.70171e-12 2.08789e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 2.369547124095843e-01 2.369547124317494e-01 2.21650e-11 4.45771e-10 2 -1.330211831492930e+00 -1.330211831477921e+00 1.50084e-11 2.73616e-10 3 -1.993856263746213e+00 -1.993856263784355e+00 3.81415e-11 1.56681e-10 ----------------------------------------------------------------------------------------------------- 26 Pd 1 1.195196670554689e+00 1.195196670515626e+00 3.90632e-11 3.49514e-10 2 -2.836925339363040e-01 -2.836925339429475e-01 6.64352e-12 1.87484e-10 3 9.125900659728212e-01 9.125900660045079e-01 3.16867e-11 1.68441e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 3.340411660853051e-01 3.340411661811173e-01 9.58122e-11 1.79309e-10 2 -1.497314383388276e+00 -1.497314383442491e+00 5.42157e-11 1.45221e-10 3 -3.362676647322735e-01 -3.362676648237019e-01 9.14284e-11 2.16509e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -1.227699540326112e+00 -1.227699540334593e+00 8.48122e-12 2.87222e-10 2 2.028132040508188e+00 2.028132040520175e+00 1.19864e-11 9.96057e-11 3 1.719769421420538e+00 1.719769421457648e+00 3.71103e-11 1.95637e-10 ----------------------------------------------------------------------------------------------------- 29 Pd 1 -2.018094201817705e+00 -2.018094201820358e+00 2.65299e-12 2.39136e-10 2 -1.176737381595659e+00 -1.176737381701838e+00 1.06180e-10 6.28806e-10 3 3.311100309068351e+00 3.311100309151739e+00 8.33884e-11 5.14004e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 7.192959640020140e-01 7.192959639771969e-01 2.48171e-11 4.11031e-11 2 8.592547075474986e-01 8.592547074844217e-01 6.30769e-11 2.00322e-10 3 1.039704390328129e+00 1.039704390376538e+00 4.84086e-11 8.50096e-11 ----------------------------------------------------------------------------------------------------- 31 Ti 1 9.435306228122324e-01 9.435306228093301e-01 2.90235e-12 3.03899e-10 2 7.308786642116262e-01 7.308786642125499e-01 9.23706e-13 2.31433e-10 3 2.263140018352242e-01 2.263140018380428e-01 2.81858e-12 8.92335e-11 ----------------------------------------------------------------------------------------------------- 32 Pd 1 7.149838597378235e-01 7.149838597045929e-01 3.32306e-11 4.63384e-10 2 4.287965903053190e-01 4.287965903553277e-01 5.00088e-11 4.06434e-10 3 -3.104413072407692e-01 -3.104413072226755e-01 1.80937e-11 6.26905e-10 ----------------------------------------------------------------------------------------------------- * 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 = 2: |F_model - F_numer| error = ----------------------- = 1.38617e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.38617e-09 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 1.38617e-09 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.