!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_000 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 4.461756305265752e-01 4.44214e-11 9.52157e-11 2 -3.065855761789613e-01 -3.065855762513215e-01 7.23602e-11 5.79753e-11 3 -3.438369847001623e-01 -3.438369847070702e-01 6.90786e-12 1.20928e-10 ----------------------------------------------------------------------------------------------------- 2 Pd 1 -1.921795827249019e-01 -1.921795827513161e-01 2.64141e-11 4.44533e-10 2 7.111047907620169e-01 7.111047907992272e-01 3.72102e-11 8.85146e-11 3 3.550720151148114e-02 3.550720152174641e-02 1.02653e-11 4.41188e-10 ----------------------------------------------------------------------------------------------------- 3 Pd 1 1.205360016987321e+00 1.205360016922842e+00 6.44784e-11 2.01100e-10 2 -5.436820889643076e-01 -5.436820889986897e-01 3.43822e-11 1.06717e-10 3 4.550002020827175e-01 4.550002020970186e-01 1.43011e-11 4.55765e-10 ----------------------------------------------------------------------------------------------------- 4 Pd 1 2.102014859865139e-01 2.102014859840771e-01 2.43675e-12 1.71082e-10 2 1.153824886357926e+00 1.153824886348779e+00 9.14691e-12 1.37637e-10 3 6.975295049529279e-01 6.975295049313476e-01 2.15803e-11 2.65646e-10 ----------------------------------------------------------------------------------------------------- 5 Pd 1 -1.060404471161045e-01 -1.060404472188686e-01 1.02764e-10 1.68362e-10 2 3.504107085357334e-01 3.504107084414075e-01 9.43259e-11 1.74834e-10 3 4.879914054861027e-01 4.879914055176500e-01 3.15473e-11 1.36666e-10 ----------------------------------------------------------------------------------------------------- 6 Pd 1 -9.709534706665104e-02 -9.709534703452703e-02 3.21240e-11 1.82150e-10 2 5.121666111448766e-01 5.121666111338258e-01 1.10508e-11 1.37846e-11 3 5.255581213290961e-01 5.255581213241404e-01 4.95570e-12 1.13594e-11 ----------------------------------------------------------------------------------------------------- 7 Pd 1 -5.060432985499036e-01 -5.060432985258548e-01 2.40488e-11 4.43495e-10 2 -3.541482008967264e+00 -3.541482008945010e+00 2.22533e-11 1.33623e-10 3 -3.866447133583737e+00 -3.866447133521126e+00 6.26117e-11 4.98312e-10 ----------------------------------------------------------------------------------------------------- 8 Pd 1 -1.957848625819353e+00 -1.957848625791366e+00 2.79865e-11 2.76169e-10 2 -2.694121119966916e+00 -2.694121119917935e+00 4.89817e-11 2.38471e-10 3 -9.896682959349850e-01 -9.896682959774363e-01 4.24514e-11 4.43483e-10 ----------------------------------------------------------------------------------------------------- 9 Pd 1 2.932293100073680e-01 2.932293100428232e-01 3.54552e-11 8.32581e-11 2 -1.312120817126624e+00 -1.312120817118678e+00 7.94675e-12 4.93452e-11 3 -6.725236788778152e-01 -6.725236788893645e-01 1.15493e-11 1.17136e-08 * ----------------------------------------------------------------------------------------------------- 10 Pd 1 -1.049945862452693e+00 -1.049945862454435e+00 1.74261e-12 1.97905e-10 2 4.643730865725963e-01 4.643730865451527e-01 2.74437e-11 1.48599e-10 3 -1.148049066277497e+00 -1.148049066266490e+00 1.10070e-11 2.35913e-10 ----------------------------------------------------------------------------------------------------- 11 Pd 1 -6.340274934672254e-01 -6.340274935157081e-01 4.84827e-11 1.34584e-10 2 -9.825907827408011e-01 -9.825907827283329e-01 1.24682e-11 4.18898e-10 3 -3.564574879167162e-01 -3.564574879238800e-01 7.16388e-12 9.25699e-11 ----------------------------------------------------------------------------------------------------- 12 Pd 1 -4.045936397704377e-01 -4.045936397695883e-01 8.49376e-13 5.42039e-11 2 1.170887979750142e+00 1.170887979756878e+00 6.73595e-12 1.84725e-10 3 3.718857160318894e-01 3.718857160140557e-01 1.78337e-11 1.44085e-10 ----------------------------------------------------------------------------------------------------- 13 Pd 1 -2.126185639296313e+00 -2.126185639296983e+00 6.69687e-13 4.22174e-10 2 -2.110715109741362e+00 -2.110715109769494e+00 2.81326e-11 1.24978e-09 3 -4.244037658196052e+00 -4.244037658243708e+00 4.76561e-11 1.02802e-10 ----------------------------------------------------------------------------------------------------- 14 Pd 1 -2.410403298828414e-01 -2.410403298762558e-01 6.58559e-12 8.75248e-11 2 8.996241983218516e-01 8.996241983063911e-01 1.54605e-11 1.84967e-10 3 2.812723956554464e-01 2.812723956620510e-01 6.60455e-12 1.82792e-10 ----------------------------------------------------------------------------------------------------- 15 Pd 1 4.697038442054041e+00 4.697038442079999e+00 2.59579e-11 7.70806e-11 2 -2.694285294160924e+00 -2.694285294152406e+00 8.51852e-12 2.86931e-10 3 1.163275754459025e+00 1.163275754452731e+00 6.29385e-12 1.22683e-10 ----------------------------------------------------------------------------------------------------- 16 Pd 1 8.284787781134051e-01 8.284787780654110e-01 4.79941e-11 8.11264e-10 2 3.128350681518711e+00 3.128350681595192e+00 7.64810e-11 4.05178e-10 3 8.983753106290081e-01 8.983753106474458e-01 1.84377e-11 2.69851e-10 ----------------------------------------------------------------------------------------------------- 17 Pd 1 -4.061454098686907e-01 -4.061454098928807e-01 2.41900e-11 6.77448e-11 2 -5.012973939769411e-01 -5.012973939556816e-01 2.12594e-11 7.16560e-10 3 -9.846937219540294e-01 -9.846937219588875e-01 4.85811e-12 1.36741e-10 ----------------------------------------------------------------------------------------------------- 18 Pd 1 6.886334401180052e-01 6.886334401689118e-01 5.09066e-11 8.01860e-10 2 1.717980257880749e+00 1.717980257940055e+00 5.93057e-11 6.65703e-11 3 3.758367885060694e-01 3.758367884787185e-01 2.73509e-11 4.54978e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 1.187025105388809e+00 1.187025105388368e+00 4.40981e-13 2.51024e-10 2 -7.673650622451951e-01 -7.673650622456274e-01 4.32321e-13 8.99778e-10 3 8.898253417270421e-02 8.898253423659952e-02 6.38953e-11 1.14424e-09 ----------------------------------------------------------------------------------------------------- 20 Pd 1 -6.439149472052798e-01 -6.439149472075621e-01 2.28240e-12 1.02867e-11 2 1.644804666684211e+00 1.644804666682560e+00 1.65068e-12 6.02693e-09 * 3 4.139079614686256e-01 4.139079614682110e-01 4.14613e-13 3.19020e-10 ----------------------------------------------------------------------------------------------------- 21 Pd 1 -7.509464459917160e-01 -7.509464459881343e-01 3.58169e-12 8.00829e-10 2 1.914155628111527e-01 1.914155628165999e-01 5.44711e-12 1.10914e-09 3 -7.665970663038410e-02 -7.665970663551508e-02 5.13098e-12 4.68683e-11 ----------------------------------------------------------------------------------------------------- 22 Pd 1 6.918346538239658e-01 6.918346538499740e-01 2.60082e-11 7.90922e-10 2 4.784037018678341e+00 4.784037018560880e+00 1.17461e-10 4.08287e-10 3 4.082974530434764e+00 4.082974530487228e+00 5.24647e-11 4.17893e-10 ----------------------------------------------------------------------------------------------------- 23 Pd 1 -6.178851032984695e-01 -6.178851032966616e-01 1.80789e-12 1.26732e-10 2 4.545779294766472e-01 4.545779294776669e-01 1.01968e-12 4.39893e-10 3 -5.076687120422380e-01 -5.076687120214903e-01 2.07476e-11 6.92809e-11 ----------------------------------------------------------------------------------------------------- 24 Pd 1 1.433003135961311e-01 1.433003136045049e-01 8.37380e-12 1.46775e-10 2 2.473658363711074e-01 2.473658363747525e-01 3.64511e-12 4.11807e-11 3 -9.575779752795094e-01 -9.575779752727239e-01 6.78546e-12 8.75283e-11 ----------------------------------------------------------------------------------------------------- 25 Pd 1 -5.620482469743164e-01 -5.620482470389043e-01 6.45879e-11 2.95373e-10 2 -9.335156363513351e-01 -9.335156363768929e-01 2.55579e-11 3.32993e-10 3 8.576839208957038e-01 8.576839208758412e-01 1.98626e-11 2.86836e-09 * ----------------------------------------------------------------------------------------------------- 26 Pd 1 -1.184233684801010e+00 -1.184233684793856e+00 7.15383e-12 2.29496e-10 2 1.389424273050106e+00 1.389424273097527e+00 4.74214e-11 9.08438e-10 3 -3.780764888169298e-01 -3.780764888605479e-01 4.36181e-11 2.87928e-10 ----------------------------------------------------------------------------------------------------- 27 Pd 1 2.467645072943484e+00 2.467645072904646e+00 3.88387e-11 1.03839e-10 2 -4.791687686438070e+00 -4.791687686459643e+00 2.15730e-11 1.36040e-10 3 6.649095815219408e-01 6.649095815397008e-01 1.77600e-11 5.91959e-10 ----------------------------------------------------------------------------------------------------- 28 Pd 1 -2.212639158915868e+00 -2.212639158907701e+00 8.16769e-12 4.73781e-11 2 2.598813001944294e+00 2.598813001977573e+00 3.32792e-11 2.58690e-10 3 -7.341920376956671e-01 -7.341920376836324e-01 1.20347e-11 2.06924e-10 ----------------------------------------------------------------------------------------------------- 29 Pd 1 -4.499725912533619e-01 -4.499725912611038e-01 7.74192e-12 2.45607e-10 2 -1.415211941771008e+00 -1.415211941823863e+00 5.28551e-11 4.42878e-10 3 2.311021405312257e+00 2.311021405371124e+00 5.88662e-11 2.32216e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 3.030399963353254e-01 3.030399963384105e-01 3.08514e-12 1.71445e-10 2 1.042446000901669e+00 1.042446000842405e+00 5.92639e-11 3.11871e-10 3 1.360850514421800e+00 1.360850514438005e+00 1.62048e-11 2.24394e-10 ----------------------------------------------------------------------------------------------------- 31 Pd 1 1.724519878738359e-01 1.724519878804808e-01 6.64491e-12 4.89061e-10 2 -7.012037448793080e-01 -7.012037449698384e-01 9.05304e-11 5.67629e-11 3 -4.107141071075447e-01 -4.107141071084162e-01 8.71470e-13 3.17643e-11 ----------------------------------------------------------------------------------------------------- 32 Pd 1 8.083716206559334e-01 8.083716206976925e-01 4.17592e-11 2.49314e-10 2 8.342567727468881e-01 8.342567727573842e-01 1.04960e-11 2.66769e-10 3 5.980402061417077e-01 5.980402061352653e-01 6.44240e-12 5.64486e-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 3.451553151804832e-01 2.77517e-12 1.09100e-10 2 1.546196741987336e-01 1.546196742026587e-01 3.92508e-12 3.31662e-11 3 3.800418312763711e-01 3.800418312766987e-01 3.27627e-13 3.45519e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -2.106481257950507e-01 -2.106481257874953e-01 7.55540e-12 1.06766e-10 2 -5.768116837357336e-02 -5.768116837378274e-02 2.09381e-13 1.91862e-11 3 1.062157277747283e+00 1.062157277725243e+00 2.20395e-11 1.18076e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 3.344690059664885e-01 3.344690059507830e-01 1.57055e-11 1.29262e-10 2 6.288512427687096e-01 6.288512427415650e-01 2.71446e-11 1.55689e-10 3 -5.583148689980935e-01 -5.583148690034830e-01 5.38958e-12 3.98963e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -4.022191063877909e-01 -4.022191063833362e-01 4.45471e-12 1.59091e-09 * 2 -1.873226499180193e+00 -1.873226499186999e+00 6.80611e-12 1.87435e-11 3 1.023358057652998e+00 1.023358057665750e+00 1.27522e-11 3.66469e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -5.881775399345706e-01 -5.881775399201450e-01 1.44256e-11 9.45333e-11 2 -8.642133087708059e-02 -8.642133086102348e-02 1.60571e-11 1.20941e-10 3 -8.949473563768970e-01 -8.949473563679414e-01 8.95561e-12 1.09567e-10 ----------------------------------------------------------------------------------------------------- 6 Ti 1 5.579844112885826e-01 5.579844113022567e-01 1.36742e-11 1.20329e-10 2 -5.025482159390191e-01 -5.025482159526775e-01 1.36584e-11 9.81376e-11 3 -3.141499455952840e-02 -3.141499456935683e-02 9.82844e-12 2.87022e-09 * ----------------------------------------------------------------------------------------------------- 7 Ti 1 2.126670655198589e+00 2.126670655202163e+00 3.57403e-12 2.58740e-11 2 -1.247375179823397e+00 -1.247375179830084e+00 6.68732e-12 2.96818e-11 3 2.741496719554125e-01 2.741496719529032e-01 2.50927e-12 7.30617e-11 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -1.653329412656381e+00 -1.653329412679905e+00 2.35236e-11 1.96717e-09 * 2 2.359808326171845e+00 2.359808326180137e+00 8.29203e-12 2.03377e-10 3 -5.923199261181634e-01 -5.923199261079132e-01 1.02502e-11 1.38035e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -4.185848310273349e-01 -4.185848310272740e-01 6.08957e-14 3.91762e-10 2 1.199436516628576e+00 1.199436516588134e+00 4.04423e-11 1.44753e-10 3 -5.875340519371368e-01 -5.875340519322372e-01 4.89964e-12 2.94096e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 8.451146124189479e-01 8.451146124293508e-01 1.04029e-11 1.29158e-10 2 -7.087799075012309e-01 -7.087799075228155e-01 2.15846e-11 1.83433e-10 3 -3.544873099665957e-01 -3.544873099805659e-01 1.39702e-11 1.80521e-09 * ----------------------------------------------------------------------------------------------------- 11 Ti 1 -1.280387218859235e+00 -1.280387218839980e+00 1.92544e-11 1.50832e-09 * 2 8.987640680147547e-01 8.987640680263228e-01 1.15681e-11 4.44645e-11 3 -2.553312380784639e+00 -2.553312380935504e+00 1.50865e-10 1.95418e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -1.741880513435197e-01 -1.741880513301489e-01 1.33707e-11 7.14434e-11 2 -4.181731871229200e-01 -4.181731870643450e-01 5.85750e-11 8.09088e-11 3 1.005710117157746e+00 1.005710117173312e+00 1.55660e-11 7.98683e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -3.150048201590778e-01 -3.150048201292883e-01 2.97896e-11 7.33685e-11 2 -1.330028822197078e+00 -1.330028822135119e+00 6.19589e-11 2.61047e-10 3 -1.810134838024231e-01 -1.810134838925025e-01 9.00794e-11 1.39493e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 8.649194611166808e-01 8.649194610952825e-01 2.13983e-11 3.58735e-09 * 2 5.044949781765059e-01 5.044949781893622e-01 1.28563e-11 1.20762e-10 3 -1.491096841763551e-01 -1.491096841782212e-01 1.86609e-12 4.45771e-11 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -4.269937528079841e-01 -4.269937528160603e-01 8.07615e-12 6.27883e-11 2 5.821535766638227e-01 5.821535765933450e-01 7.04777e-11 1.77863e-10 3 -7.772816028532491e-01 -7.772816028497589e-01 3.49021e-12 2.42929e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.984291968146902e-01 -1.984291968374027e-01 2.27125e-11 1.38483e-09 * 2 8.456326649517758e-01 8.456326649309611e-01 2.08147e-11 1.83239e-10 3 8.427329791410466e-01 8.427329791472044e-01 6.15774e-12 2.62404e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 5.203043413193907e-01 5.203043412727325e-01 4.66582e-11 2.21307e-10 2 3.258403825011406e-01 3.258403824850036e-01 1.61370e-11 3.80412e-11 3 1.316852477586735e-01 1.316852477548302e-01 3.84334e-12 4.52872e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -1.106602916488875e+00 -1.106602916455380e+00 3.34948e-11 2.06657e-11 2 -3.076010758516267e+00 -3.076010758321163e+00 1.95104e-10 1.26324e-10 3 -1.937423072160965e+00 -1.937423072100763e+00 6.02023e-11 2.89472e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -7.868730976318123e-01 -7.868730975670334e-01 6.47790e-11 1.19662e-10 2 -7.873588845937294e-01 -7.873588846013939e-01 7.66454e-12 7.88438e-11 3 1.331785769077335e-01 1.331785768154952e-01 9.22384e-11 2.65875e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -6.423122662877450e-01 -6.423122662749682e-01 1.27768e-11 2.94048e-10 2 -1.036484695951653e+00 -1.036484695992165e+00 4.05111e-11 9.84843e-11 3 8.420170243000480e-01 8.420170242458188e-01 5.42292e-11 6.43345e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 -4.927875732066326e-01 -4.927875732392937e-01 3.26612e-11 1.90850e-10 2 4.967563674306605e-01 4.967563674807827e-01 5.01222e-11 1.55758e-10 3 9.176039938519600e-01 9.176039938637139e-01 1.17539e-11 3.78264e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -8.424360871701171e-01 -8.424360872126798e-01 4.25627e-11 1.46395e-09 * 2 -8.075377514514299e-01 -8.075377513846799e-01 6.67500e-11 2.89013e-10 3 8.437995952559473e-01 8.437995952782550e-01 2.23077e-11 4.86555e-11 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -3.327000460660524e-01 -3.327000460802425e-01 1.41901e-11 1.42530e-10 2 3.530219103418351e-01 3.530219103334398e-01 8.39528e-12 2.59628e-10 3 -2.820643620520800e-01 -2.820643620589928e-01 6.91275e-12 2.44320e-11 ----------------------------------------------------------------------------------------------------- 24 Ti 1 2.556570865389715e+00 2.556570865409627e+00 1.99116e-11 3.32023e-10 2 1.972088762700168e-01 1.972088762723881e-01 2.37124e-12 8.91374e-11 3 4.023209539592778e-01 4.023209539698955e-01 1.06177e-11 1.05172e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -7.980476478263869e-01 -7.980476478630036e-01 3.66167e-11 2.38010e-10 2 1.533096816643520e+00 1.533096816651234e+00 7.71450e-12 1.08526e-10 3 -7.286095384306355e-01 -7.286095384107260e-01 1.99095e-11 7.41934e-11 ----------------------------------------------------------------------------------------------------- 26 Ti 1 -7.589555329493183e-01 -7.589555329576163e-01 8.29803e-12 5.34713e-11 2 1.244638076822871e+00 1.244638076905412e+00 8.25409e-11 2.57492e-10 3 -8.842745012070279e-01 -8.842745011524525e-01 5.45753e-11 9.41108e-11 ----------------------------------------------------------------------------------------------------- 27 Ti 1 -7.675890425133597e-01 -7.675890424389196e-01 7.44401e-11 4.08036e-10 2 4.284655472903648e-01 4.284655472798049e-01 1.05599e-11 1.19749e-09 * 3 2.053733998484312e+00 2.053733998393062e+00 9.12497e-11 1.95306e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 3.456968347702066e-01 3.456968347744325e-01 4.22590e-12 1.33521e-10 2 -3.972266660454764e-01 -3.972266660433679e-01 2.10842e-12 4.30040e-11 3 -7.021573000925964e-01 -7.021573000990451e-01 6.44873e-12 4.26768e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 3.134653663241799e+00 3.134653663273420e+00 3.16209e-11 3.18296e-09 * 2 1.207800692379010e-01 1.207800692338613e-01 4.03973e-12 7.23945e-11 3 7.073032317986029e-01 7.073032318665972e-01 6.79943e-11 4.46441e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 -2.931959662960718e-02 -2.931959664065883e-02 1.10517e-11 2.57775e-10 2 2.096459682392864e-01 2.096459682531801e-01 1.38937e-11 7.23647e-11 3 5.885225796203619e-01 5.885225796059644e-01 1.43975e-11 5.71905e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 1.572071028271698e-01 1.572071028887971e-01 6.16272e-11 3.39046e-10 2 -3.355528542060427e-01 -3.355528542103252e-01 4.28246e-12 8.36714e-10 3 -3.836236241111651e-01 -3.836236241405727e-01 2.94075e-11 1.14382e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 4.368395938347114e-01 4.368395938636122e-01 2.89008e-11 1.58383e-11 2 5.811908594267704e-01 5.811908594087832e-01 1.79872e-11 1.27645e-09 * 3 3.895729207597775e-01 3.895729207736618e-01 1.38843e-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 = ----------------------- = 6.92592e-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 -3.168167018906798e-02 2.97490e-12 1.02825e-11 2 -1.008351687059506e+00 -1.008351687077462e+00 1.79561e-11 3.59834e-11 3 -1.073572558463306e+00 -1.073572558463413e+00 1.06581e-13 1.81069e-10 ----------------------------------------------------------------------------------------------------- 2 Pd 1 1.692655108144503e+00 1.692655108147201e+00 2.69762e-12 1.54858e-10 2 -2.017819917761137e+00 -2.017819917698295e+00 6.28417e-11 5.00410e-10 3 -1.126338993693921e+00 -1.126338993707455e+00 1.35341e-11 1.98252e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -2.183092537806762e+00 -2.183092537809165e+00 2.40252e-12 1.77238e-10 2 -3.312966046858146e-02 -3.312966047924415e-02 1.06627e-11 4.63815e-11 3 5.513756433806632e-01 5.513756433564696e-01 2.41936e-11 3.97898e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -1.357185080451433e+00 -1.357185080512037e+00 6.06040e-11 8.62286e-11 2 1.202467384424962e+00 1.202467384481225e+00 5.62632e-11 4.46352e-11 3 1.600063165674216e+00 1.600063165659122e+00 1.50944e-11 8.05849e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 1.572215723676643e+00 1.572215723671215e+00 5.42766e-12 3.73244e-11 2 2.867205520411780e-01 2.867205520582776e-01 1.70997e-11 1.03207e-10 3 -1.374765158944937e+00 -1.374765158943738e+00 1.19926e-12 7.51195e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -4.668677149555021e-01 -4.668677149581841e-01 2.68197e-12 9.55991e-11 2 1.757796621493708e-01 1.757796621475690e-01 1.80184e-12 2.73525e-10 3 3.765599250140551e-01 3.765599250576636e-01 4.36085e-11 8.00285e-11 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -1.590550275955201e-01 -1.590550275995646e-01 4.04449e-12 1.05941e-10 2 -5.342192206435015e-01 -5.342192206517079e-01 8.20644e-12 9.22372e-11 3 -3.103366818646440e-01 -3.103366818644726e-01 1.71418e-13 1.67361e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.043586410657960e+00 1.043586410695167e+00 3.72067e-11 9.25893e-11 2 -1.327434408536152e+00 -1.327434408491247e+00 4.49050e-11 1.98217e-10 3 -3.075432613808301e+00 -3.075432613758540e+00 4.97611e-11 6.85807e-11 ----------------------------------------------------------------------------------------------------- 9 Pd 1 -1.104080326352690e+00 -1.104080326352736e+00 4.61853e-14 1.48803e-10 2 5.520133356249084e-01 5.520133355628466e-01 6.20618e-11 2.59846e-10 3 2.742001398556543e-01 2.742001398800314e-01 2.43771e-11 9.68114e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 5.407014074208286e-01 5.407014074157054e-01 5.12324e-12 6.68896e-11 2 -2.527771796570920e-01 -2.527771796627536e-01 5.66164e-12 3.17599e-09 * 3 4.509648018585469e-01 4.509648018410796e-01 1.74674e-11 4.02604e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 2.412643720129721e-01 2.412643719998378e-01 1.31343e-11 5.01317e-11 2 3.603173092830051e+00 3.603173092821107e+00 8.94396e-12 8.86691e-10 3 4.495875345585843e-02 4.495875340389833e-02 5.19601e-11 7.52092e-10 ----------------------------------------------------------------------------------------------------- 12 Pd 1 -8.119628674297654e-01 -8.119628674533422e-01 2.35768e-11 1.17257e-10 2 -6.131951406528667e-01 -6.131951406378165e-01 1.50502e-11 2.69329e-11 3 -1.144606972992512e+00 -1.144606972996306e+00 3.79408e-12 8.53224e-11 ----------------------------------------------------------------------------------------------------- 13 Pd 1 -9.457114906986264e-02 -9.457114906804685e-02 1.81578e-12 1.71083e-10 2 5.917372350130714e-01 5.917372350153789e-01 2.30749e-12 9.88250e-09 * 3 8.822291047791303e-01 8.822291048087656e-01 2.96353e-11 1.86996e-11 ----------------------------------------------------------------------------------------------------- 14 Pd 1 -6.075618863471794e-01 -6.075618863449130e-01 2.26641e-12 1.38695e-10 2 -4.539024886465922e-01 -4.539024886501331e-01 3.54089e-12 3.97962e-11 3 5.057116346791066e-01 5.057116346848258e-01 5.71920e-12 1.94874e-10 ----------------------------------------------------------------------------------------------------- 15 Pd 1 3.698990388507461e+00 3.698990388495238e+00 1.22231e-11 2.37301e-10 2 -2.155035836373107e+00 -2.155035836388208e+00 1.51013e-11 4.95896e-10 3 -2.934615359702239e+00 -2.934615359686476e+00 1.57629e-11 1.26247e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -2.467537311785853e+00 -2.467537311809559e+00 2.37059e-11 1.50530e-10 2 2.709896974291002e+00 2.709896974250664e+00 4.03380e-11 4.08781e-10 3 -2.242876258893003e+00 -2.242876258882512e+00 1.04912e-11 4.85971e-11 ----------------------------------------------------------------------------------------------------- 17 Pd 1 5.193750875952033e-01 5.193750876015891e-01 6.38578e-12 1.58209e-10 2 7.712461840990464e-02 7.712461851681217e-02 1.06908e-10 2.18814e-10 3 4.176008530290519e-01 4.176008530957527e-01 6.67008e-11 6.10024e-10 ----------------------------------------------------------------------------------------------------- 18 Pd 1 -1.161384622435615e+00 -1.161384622648969e+00 2.13354e-10 1.68563e-08 * 2 -1.530144474835305e+00 -1.530144474804504e+00 3.08009e-11 1.14216e-09 * 3 1.513395231418782e+00 1.513395231367221e+00 5.15612e-11 2.10998e-10 ----------------------------------------------------------------------------------------------------- 19 Pd 1 1.542183226850585e+00 1.542183226839238e+00 1.13463e-11 6.86418e-11 2 -1.007521180134163e+00 -1.007521179991793e+00 1.42369e-10 5.93078e-10 3 -4.868495303178539e-01 -4.868495302900417e-01 2.78121e-11 1.33444e-10 ----------------------------------------------------------------------------------------------------- 20 Pd 1 -8.712194175616579e-01 -8.712194175431950e-01 1.84629e-11 5.79712e-11 2 1.655582069545493e+00 1.655582069436270e+00 1.09224e-10 8.44338e-11 3 -4.516252519112273e-01 -4.516252519488781e-01 3.76508e-11 4.13856e-09 * ----------------------------------------------------------------------------------------------------- 21 Ti 1 1.389578550997197e+00 1.389578550930091e+00 6.71054e-11 1.35401e-10 2 9.675817516168413e-01 9.675817515746192e-01 4.22221e-11 1.31691e-09 * 3 1.797502558869994e+00 1.797502558896907e+00 2.69134e-11 1.67030e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -2.986596307825544e-01 -2.986596307609242e-01 2.16301e-11 2.47146e-10 2 3.869403034219076e-01 3.869403034549475e-01 3.30399e-11 2.65144e-10 3 7.334133869275216e-01 7.334133869346456e-01 7.12408e-12 1.77073e-10 ----------------------------------------------------------------------------------------------------- 23 Pd 1 -5.360558395261692e-01 -5.360558395605625e-01 3.43933e-11 1.26156e-10 2 6.338229145173764e-01 6.338229145350280e-01 1.76517e-11 1.26033e-09 * 3 -6.510023263148673e-01 -6.510023263158271e-01 9.59788e-13 2.10751e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -9.878444470285782e-01 -9.878444470064653e-01 2.21129e-11 2.40201e-11 2 -1.668414571277526e+00 -1.668414571321656e+00 4.41300e-11 2.81340e-10 3 1.155133555058426e+00 1.155133555067126e+00 8.70060e-12 2.08791e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 2.369547124095843e-01 2.369547124317492e-01 2.21649e-11 4.45771e-10 2 -1.330211831492930e+00 -1.330211831477920e+00 1.50095e-11 2.73616e-10 3 -1.993856263746213e+00 -1.993856263784353e+00 3.81397e-11 1.56680e-10 ----------------------------------------------------------------------------------------------------- 26 Pd 1 1.195196670554689e+00 1.195196670515625e+00 3.90641e-11 3.49513e-10 2 -2.836925339363040e-01 -2.836925339429474e-01 6.64335e-12 1.87484e-10 3 9.125900659728212e-01 9.125900660045071e-01 3.16859e-11 1.68441e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 3.340411660853051e-01 3.340411661811170e-01 9.58119e-11 1.79309e-10 2 -1.497314383388276e+00 -1.497314383442490e+00 5.42149e-11 1.45221e-10 3 -3.362676647322735e-01 -3.362676648237022e-01 9.14288e-11 2.16510e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -1.227699540326112e+00 -1.227699540334591e+00 8.47966e-12 2.87220e-10 2 2.028132040508188e+00 2.028132040520172e+00 1.19842e-11 9.96065e-11 3 1.719769421420538e+00 1.719769421457647e+00 3.71092e-11 1.95636e-10 ----------------------------------------------------------------------------------------------------- 29 Pd 1 -2.018094201817705e+00 -2.018094201820356e+00 2.65121e-12 2.39137e-10 2 -1.176737381595659e+00 -1.176737381666400e+00 7.07419e-11 5.74970e-10 3 3.311100309068351e+00 3.311100309151736e+00 8.33857e-11 5.14004e-10 ----------------------------------------------------------------------------------------------------- 30 Pd 1 7.192959640020140e-01 7.192959639771963e-01 2.48177e-11 4.11032e-11 2 8.592547075474986e-01 8.592547074844209e-01 6.30777e-11 2.00322e-10 3 1.039704390328129e+00 1.039704390376537e+00 4.84075e-11 8.50100e-11 ----------------------------------------------------------------------------------------------------- 31 Ti 1 9.435306228122324e-01 9.435306228093292e-01 2.90323e-12 3.03899e-10 2 7.308786642116262e-01 7.308786642125502e-01 9.24039e-13 2.31433e-10 3 2.263140018352242e-01 2.263140018380426e-01 2.81836e-12 8.92334e-11 ----------------------------------------------------------------------------------------------------- 32 Pd 1 7.149838597378235e-01 7.149838597045923e-01 3.32312e-11 4.63384e-10 2 4.287965903053190e-01 4.287965903553272e-01 5.00083e-11 4.06434e-10 3 -3.104413072407692e-01 -3.104413072226753e-01 1.80940e-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.