!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_SaLee_2008_FeTi__MO_260546967793_000 Supported species : Fe 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 = Fe | a0 = 3.611098289489746 | (Configuration in file "config-Fe.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Fe 1 3.603623242205600e-01 3.603623242526416e-01 3.20816e-11 1.66824e-10 2 -5.247648672329353e-02 -5.247648672204230e-02 1.25122e-12 1.87767e-11 3 -4.185879519906143e-01 -4.185879519878373e-01 2.77700e-12 1.05624e-10 ----------------------------------------------------------------------------------------------------- 2 Fe 1 -5.849824601907671e-01 -5.849824601903703e-01 3.96794e-13 1.64389e-10 2 3.298315232486727e-01 3.298315232474911e-01 1.18155e-12 1.78552e-11 3 9.219101184428434e-01 9.219101184452853e-01 2.44182e-12 2.96961e-10 ----------------------------------------------------------------------------------------------------- 3 Fe 1 1.455209062547537e+00 1.455209062549991e+00 2.45359e-12 1.50045e-10 2 2.389431181564790e-01 2.389431181495944e-01 6.88455e-12 4.68438e-11 3 -1.418157203208000e+00 -1.418157203244590e+00 3.65896e-11 5.11510e-10 ----------------------------------------------------------------------------------------------------- 4 Fe 1 6.632933183361843e-01 6.632933183030016e-01 3.31827e-11 4.47188e-11 2 3.479358700341447e-01 3.479358700398215e-01 5.67685e-12 9.63976e-11 3 5.349212291041032e-01 5.349212291036824e-01 4.20775e-13 5.64226e-10 ----------------------------------------------------------------------------------------------------- 5 Fe 1 9.632547229909352e-02 9.632547229914656e-02 5.30409e-14 7.80672e-11 2 2.986799887355198e-01 2.986799887291165e-01 6.40327e-12 1.31563e-10 3 6.514033341897761e-01 6.514033341873640e-01 2.41218e-12 6.98738e-11 ----------------------------------------------------------------------------------------------------- 6 Fe 1 -7.789670720446794e-01 -7.789670720338688e-01 1.08106e-11 4.36426e-11 2 5.688901240177245e-01 5.688901240192562e-01 1.53166e-12 2.08238e-10 3 4.825926340822718e-01 4.825926340647411e-01 1.75308e-11 4.26638e-10 ----------------------------------------------------------------------------------------------------- 7 Fe 1 4.218555460323529e-01 4.218555460339544e-01 1.60150e-12 6.26511e-11 2 -2.492627529752216e+00 -2.492627529796160e+00 4.39431e-11 4.48802e-09 * 3 -2.741122315279289e+00 -2.741122315279356e+00 6.75016e-14 8.95843e-10 ----------------------------------------------------------------------------------------------------- 8 Fe 1 -1.833076657239696e+00 -1.833076657282113e+00 4.24165e-11 4.42017e-10 2 -2.189949489580612e+00 -2.189949489581851e+00 1.23990e-12 8.69487e-10 3 -8.914981448841591e-01 -8.914981448557999e-01 2.83592e-11 9.68857e-11 ----------------------------------------------------------------------------------------------------- 9 Fe 1 1.904453720901564e-01 1.904453720987969e-01 8.64053e-12 1.86100e-10 2 -1.667608481666403e+00 -1.667608481728018e+00 6.16149e-11 5.25728e-10 3 -1.468865679504995e+00 -1.468865679611019e+00 1.06023e-10 2.86346e-10 ----------------------------------------------------------------------------------------------------- 10 Fe 1 -1.353660477501910e+00 -1.353660477513664e+00 1.17539e-11 1.48632e-10 2 1.084709563278845e+00 1.084709563244072e+00 3.47731e-11 4.03029e-11 3 -1.486882946689672e+00 -1.486882946739163e+00 4.94909e-11 1.47574e-10 ----------------------------------------------------------------------------------------------------- 11 Fe 1 -8.590605446167346e-01 -8.590605446771640e-01 6.04293e-11 1.35980e-10 2 -1.392544411742545e+00 -1.392544411735815e+00 6.73017e-12 4.60096e-11 3 1.268545949464072e+00 1.268545949421550e+00 4.25215e-11 4.45803e-11 ----------------------------------------------------------------------------------------------------- 12 Fe 1 4.246507193524345e-01 4.246507194066241e-01 5.41897e-11 4.99439e-11 2 1.557594577317228e+00 1.557594577288444e+00 2.87839e-11 9.97517e-10 3 1.157018899688556e+00 1.157018899801215e+00 1.12658e-10 5.40428e-10 ----------------------------------------------------------------------------------------------------- 13 Fe 1 -1.044793931914121e+00 -1.044793931903847e+00 1.02733e-11 7.26503e-11 2 -2.238075668644872e+00 -2.238075668637544e+00 7.32792e-12 7.76916e-11 3 -3.166655779486183e+00 -3.166655779420373e+00 6.58100e-11 8.75287e-11 ----------------------------------------------------------------------------------------------------- 14 Fe 1 4.035957051345983e-01 4.035957051360310e-01 1.43269e-12 1.82457e-10 2 6.067157374653415e-01 6.067157374706815e-01 5.34006e-12 2.54811e-09 * 3 1.558408620046260e-01 1.558408619367702e-01 6.78559e-11 1.20255e-10 ----------------------------------------------------------------------------------------------------- 15 Fe 1 3.130302945203054e+00 3.130302945201394e+00 1.65912e-12 3.79936e-11 2 2.849132774376489e-01 2.849132774040470e-01 3.36018e-11 1.65670e-10 3 1.090789084348350e+00 1.090789084367387e+00 1.90363e-11 2.38293e-10 ----------------------------------------------------------------------------------------------------- 16 Fe 1 1.278199004172152e+00 1.278199004175333e+00 3.18101e-12 6.25999e-09 * 2 2.095665174793912e+00 2.095665174711745e+00 8.21672e-11 1.29513e-08 * 3 1.397280795405740e+00 1.397280795375036e+00 3.07037e-11 5.30112e-10 ----------------------------------------------------------------------------------------------------- 17 Fe 1 -2.067680831094391e+00 -2.067680831098068e+00 3.67706e-12 6.96674e-11 2 -5.587536405941411e-01 -5.587536406081929e-01 1.40518e-11 1.82663e-10 3 3.623927912163233e-01 3.623927911882696e-01 2.80538e-11 6.17362e-10 ----------------------------------------------------------------------------------------------------- 18 Fe 1 1.604968490922476e+00 1.604968490860864e+00 6.16120e-11 2.91942e-10 2 1.556719094490185e+00 1.556719094478947e+00 1.12381e-11 8.86241e-10 3 5.350815611008093e-01 5.350815611193713e-01 1.85620e-11 1.14662e-10 ----------------------------------------------------------------------------------------------------- 19 Fe 1 4.458588583059506e-01 4.458588583635926e-01 5.76421e-11 4.98631e-11 2 4.777005016481743e-02 4.777005016443560e-02 3.81833e-13 2.36627e-10 3 9.239102160699095e-02 9.239102172000362e-02 1.13013e-10 4.13692e-10 ----------------------------------------------------------------------------------------------------- 20 Fe 1 6.689443379725960e-01 6.689443379635686e-01 9.02745e-12 1.39538e-10 2 4.705362436726568e-01 4.705362436740230e-01 1.36618e-12 3.85969e-09 * 3 -4.757480076909772e-01 -4.757480076964115e-01 5.43421e-12 1.09330e-10 ----------------------------------------------------------------------------------------------------- 21 Fe 1 -1.071097557918255e+00 -1.071097557987789e+00 6.95342e-11 5.92528e-10 2 4.580285098153313e-01 4.580285098257251e-01 1.03937e-11 2.68113e-10 3 7.810783486824354e-01 7.810783486837268e-01 1.29141e-12 1.35245e-10 ----------------------------------------------------------------------------------------------------- 22 Fe 1 1.532123205972570e-01 1.532123205950443e-01 2.21276e-12 3.40029e-10 2 2.405082355094045e+00 2.405082355142764e+00 4.87193e-11 1.34206e-10 3 2.723712581021344e+00 2.723712581083961e+00 6.26166e-11 4.07028e-10 ----------------------------------------------------------------------------------------------------- 23 Fe 1 -6.248680306657228e-01 -6.248680306578710e-01 7.85183e-12 1.34036e-10 2 6.522567567083911e-01 6.522567566865913e-01 2.17998e-11 2.52738e-09 * 3 -4.601760389716347e-01 -4.601760390417817e-01 7.01469e-11 2.22746e-10 ----------------------------------------------------------------------------------------------------- 24 Fe 1 3.782052608185800e-01 3.782052608835765e-01 6.49965e-11 9.26189e-11 2 4.735566398885263e-01 4.735566399754039e-01 8.68776e-11 1.57241e-10 3 -8.725848413357257e-01 -8.725848413884874e-01 5.27617e-11 1.14657e-09 ----------------------------------------------------------------------------------------------------- 25 Fe 1 -3.965816290092370e-01 -3.965816290156540e-01 6.41698e-12 9.29867e-09 * 2 -7.145865381791174e-01 -7.145865381835287e-01 4.41125e-12 4.14102e-10 3 7.434328379928627e-01 7.434328380746699e-01 8.18071e-11 6.40603e-10 ----------------------------------------------------------------------------------------------------- 26 Fe 1 -1.468473230686475e+00 -1.468473230676801e+00 9.67382e-12 3.63720e-10 2 7.101984097469537e-01 7.101984096722036e-01 7.47501e-11 7.35353e-10 3 -1.173602709651600e+00 -1.173602709363547e+00 2.88052e-10 1.07772e-10 ----------------------------------------------------------------------------------------------------- 27 Fe 1 1.495635144152422e+00 1.495635144180552e+00 2.81302e-11 3.81754e-10 2 -3.120679624181529e+00 -3.120679624203229e+00 2.17000e-11 7.86875e-09 * 3 4.522288385257392e-02 4.522288383710198e-02 1.54719e-11 5.27687e-10 ----------------------------------------------------------------------------------------------------- 28 Fe 1 -1.544951144393833e+00 -1.544951144418655e+00 2.48217e-11 2.94881e-10 2 1.436879874527019e+00 1.436879874525792e+00 1.22680e-12 6.09741e-11 3 -3.877380329367734e-01 -3.877380329335731e-01 3.20033e-12 9.39292e-11 ----------------------------------------------------------------------------------------------------- 29 Fe 1 -3.777063894883829e-01 -3.777063894993721e-01 1.09892e-11 2.39376e-10 2 -8.699469567705249e-01 -8.699469568111549e-01 4.06299e-11 1.93361e-09 * 3 1.428686716668068e+00 1.428686716668193e+00 1.24789e-13 7.15135e-10 ----------------------------------------------------------------------------------------------------- 30 Fe 1 -5.378711731498727e-01 -5.378711731388467e-01 1.10260e-11 2.97500e-09 * 2 5.597887978504629e-02 5.597887977757045e-02 7.47584e-12 1.37198e-10 3 -4.541662693881286e-02 -4.541662691419765e-02 2.46152e-11 4.87491e-10 ----------------------------------------------------------------------------------------------------- 31 Fe 1 8.211984218810758e-02 8.211984208312720e-02 1.04980e-10 5.00312e-10 2 -9.844091327653259e-01 -9.844091327497555e-01 1.55704e-11 4.18207e-10 3 -7.903166683734768e-02 -7.903166685134436e-02 1.39967e-11 2.39485e-11 ----------------------------------------------------------------------------------------------------- 32 Fe 1 1.290587405568565e+00 1.290587405471061e+00 9.75042e-11 2.41875e-10 2 6.007721922220906e-01 6.007721922352154e-01 1.31248e-11 8.68338e-11 3 7.137662965340361e-01 7.137662963691844e-01 1.64852e-10 3.20536e-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 = 31, direction = 1: |F_model - F_numer| error = ----------------------- = 1.27838e-09 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 = 4.132986068725586 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 -3.981911222296210e-01 -3.981911221736066e-01 5.60144e-11 1.79947e-10 2 -5.858486393983364e-02 -5.858486389143606e-02 4.83976e-11 7.31705e-11 3 4.785969435132106e-02 4.785969433432700e-02 1.69941e-11 1.48679e-09 * ----------------------------------------------------------------------------------------------------- 2 Ti 1 8.110585202963705e-01 8.110585203324805e-01 3.61100e-11 4.64603e-10 2 5.838952298103284e-01 5.838952298082769e-01 2.05147e-12 2.45824e-11 3 6.365810133007581e-01 6.365810132959173e-01 4.84079e-12 1.36305e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 5.716928616389085e-01 5.716928616671383e-01 2.82298e-11 4.92325e-10 2 5.255737086883207e-01 5.255737085942089e-01 9.41117e-11 2.81124e-10 3 3.904335641122291e-01 3.904335641352935e-01 2.30644e-11 1.22030e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 -3.030393299020945e-01 -3.030393299387644e-01 3.66699e-11 1.00068e-10 2 -2.951169920360069e-01 -2.951169920372926e-01 1.28575e-12 1.50387e-10 3 4.734532143255326e-01 4.734532143191244e-01 6.40815e-12 1.18005e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -4.927275514299854e-01 -4.927275514325692e-01 2.58382e-12 4.64485e-11 2 6.004433183711130e-01 6.004433183536505e-01 1.74625e-11 1.02418e-10 3 5.639158938471314e-01 5.639158938416823e-01 5.44909e-12 2.49181e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -4.630912443903060e-01 -4.630912443737254e-01 1.65806e-11 1.01751e-11 2 4.129124081369573e-01 4.129124081028409e-01 3.41164e-11 5.57759e-10 3 1.003933076173099e+00 1.003933076067172e+00 1.05927e-10 1.40370e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -4.932024044436356e-01 -4.932024044417710e-01 1.86456e-12 6.55466e-10 2 6.292895560491401e-01 6.292895560482237e-01 9.16378e-13 1.91426e-10 3 3.142478957779478e-01 3.142478957633194e-01 1.46284e-11 1.11730e-09 * ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.435588878244638e+00 1.435588878170141e+00 7.44971e-11 5.09271e-10 2 -1.441762227352095e+00 -1.441762227312090e+00 4.00056e-11 3.13249e-10 3 -5.510079829951051e-01 -5.510079830157375e-01 2.06324e-11 4.03430e-11 ----------------------------------------------------------------------------------------------------- 9 Ti 1 4.537396921234494e-01 4.537396921014110e-01 2.20385e-11 7.02694e-11 2 5.191198035486853e-01 5.191198035272754e-01 2.14099e-11 7.24139e-11 3 2.949076787452757e-01 2.949076787313014e-01 1.39744e-11 6.65978e-11 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -1.502600375477966e-01 -1.502600375134461e-01 3.43505e-11 1.98102e-10 2 -7.750500569614507e-02 -7.750500570382612e-02 7.68105e-12 4.04514e-11 3 3.333319776520361e-01 3.333319776390330e-01 1.30032e-11 2.07004e-10 ----------------------------------------------------------------------------------------------------- 11 Ti 1 -2.056746542123032e+00 -2.056746542136557e+00 1.35256e-11 2.13059e-09 * 2 -7.159621598219935e-01 -7.159621598956378e-01 7.36443e-11 3.25649e-10 3 8.979227660893543e-01 8.979227661428042e-01 5.34499e-11 6.83569e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 4.120012407314008e-01 4.120012407437316e-01 1.23307e-11 2.83417e-11 2 -6.116331941672382e-01 -6.116331941660990e-01 1.13920e-12 8.27325e-11 3 -6.382895142241689e-01 -6.382895141904245e-01 3.37445e-11 1.20130e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -8.478219502143512e-02 -8.478219500565592e-02 1.57792e-11 2.04980e-10 2 -8.075194470359288e-01 -8.075194470497828e-01 1.38540e-11 1.10906e-10 3 -4.511208235318699e-01 -4.511208235599437e-01 2.80738e-11 1.22897e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 8.671153252864117e-01 8.671153252952838e-01 8.87213e-12 7.70618e-11 2 1.163031597944259e-01 1.163031598059972e-01 1.15713e-11 8.97856e-10 3 1.490471106209897e-01 1.490471106407618e-01 1.97721e-11 1.14167e-09 * ----------------------------------------------------------------------------------------------------- 15 Ti 1 -5.710584876651645e-01 -5.710584876793378e-01 1.41732e-11 1.40296e-09 * 2 2.754153779282719e-01 2.754153779449856e-01 1.67137e-11 1.25705e-10 3 -5.596991627794953e-01 -5.596991626823387e-01 9.71566e-11 2.85340e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 5.741465867007050e-01 5.741465868336247e-01 1.32920e-10 2.91672e-10 2 6.211905751706310e-01 6.211905751739879e-01 3.35687e-12 2.15578e-10 3 -8.429158056508750e-01 -8.429158056428238e-01 8.05123e-12 1.94480e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 7.578396191009750e-01 7.578396190880616e-01 1.29133e-11 5.34061e-11 2 6.304003736202055e-01 6.304003736768958e-01 5.66903e-11 3.75573e-11 3 2.235683786391336e-01 2.235683786571780e-01 1.80444e-11 1.17517e-10 ----------------------------------------------------------------------------------------------------- 18 Ti 1 -2.028272201494240e+00 -2.028272201644105e+00 1.49865e-10 5.01404e-10 2 -8.416890347474080e-01 -8.416890347045350e-01 4.28729e-11 3.39384e-10 3 -2.549433734122867e+00 -2.549433734175247e+00 5.23794e-11 2.71762e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -7.338544068442028e-01 -7.338544068446129e-01 4.10116e-13 7.53173e-11 2 4.313278637039763e-01 4.313278637830559e-01 7.90796e-11 1.30164e-10 3 -1.580642242340556e-01 -1.580642242335943e-01 4.61325e-13 1.63874e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -5.567986098331233e-01 -5.567986099073484e-01 7.42251e-11 2.06469e-10 2 -1.334088631092104e+00 -1.334088631075524e+00 1.65798e-11 1.15535e-10 3 3.066954803800415e-01 3.066954802604498e-01 1.19592e-10 3.38355e-11 ----------------------------------------------------------------------------------------------------- 21 Ti 1 5.229770374777505e-01 5.229770375172050e-01 3.94546e-11 2.42742e-09 * 2 4.426394394748346e-01 4.426394394519799e-01 2.28547e-11 8.12418e-10 3 -7.656207180552524e-01 -7.656207180896719e-01 3.44195e-11 4.90292e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 -2.191782234868851e-01 -2.191782234635424e-01 2.33427e-11 1.97627e-10 2 -1.296861969399830e+00 -1.296861969396620e+00 3.20988e-12 1.03921e-10 3 -9.719817231331289e-01 -9.719817231433938e-01 1.02649e-11 8.95596e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -5.666127221814704e-02 -5.666127221608047e-02 2.06657e-12 5.14178e-11 2 2.339849032814788e-01 2.339849032895667e-01 8.08792e-12 1.62191e-10 3 -5.060673380476268e-01 -5.060673380402289e-01 7.39797e-12 1.90490e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 1.907493888993761e+00 1.907493888991360e+00 2.40030e-12 3.88205e-10 2 -8.180800589890801e-01 -8.180800590903330e-01 1.01253e-10 1.24085e-10 3 1.623909844866900e+00 1.623909844854992e+00 1.19080e-11 1.94173e-09 * ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.598035090903727e+00 -1.598035090923099e+00 1.93718e-11 2.18800e-09 * 2 -1.199412503517838e+00 -1.199412503526256e+00 8.41793e-12 4.13804e-09 * 3 -2.550573063861078e+00 -2.550573063856816e+00 4.26148e-12 4.89122e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 1.866198909452567e+00 1.866198909433405e+00 1.91616e-11 3.09807e-10 2 1.129655451730436e+00 1.129655451719898e+00 1.05376e-11 1.41767e-09 * 3 -1.819206408898330e+00 -1.819206408979888e+00 8.15588e-11 2.56884e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 2.465080926039452e+00 2.465080926139703e+00 1.00251e-10 3.12255e-10 2 -7.743137916185872e-01 -7.743137916739755e-01 5.53884e-11 1.40578e-10 3 1.933190846055366e+00 1.933190846070818e+00 1.54519e-11 1.00276e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -1.986254493004968e+00 -1.986254492972733e+00 3.22349e-11 1.00586e-10 2 2.080595549469288e+00 2.080595549465721e+00 3.56648e-12 8.02129e-10 3 1.995734290019105e+00 1.995734290043469e+00 2.43638e-11 4.03448e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -8.981261588990687e-01 -8.981261588965690e-01 2.49967e-12 5.99101e-11 2 5.282013718887764e-01 5.282013718703065e-01 1.84699e-11 2.30049e-10 3 3.494019838686939e-01 3.494019838765619e-01 7.86793e-12 9.20456e-11 ----------------------------------------------------------------------------------------------------- 30 Ti 1 2.160797853911847e-01 2.160797853610101e-01 3.01746e-11 1.75645e-10 2 -1.607187812001606e-01 -1.607187811736475e-01 2.65132e-11 3.49412e-10 3 7.177338933506068e-01 7.177338933482492e-01 2.35756e-12 8.89739e-11 ----------------------------------------------------------------------------------------------------- 31 Ti 1 1.390201063370505e+00 1.390201063372932e+00 2.42673e-12 2.19762e-11 2 -3.132406778871402e-01 -3.132406778820600e-01 5.08016e-12 1.36413e-10 3 6.092881847406868e-01 6.092881847389261e-01 1.76070e-12 7.61746e-12 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -1.160934963410646e+00 -1.160934963447085e+00 3.64393e-11 3.33733e-10 2 9.855412478345211e-01 9.855412478169487e-01 1.75724e-11 3.35885e-10 3 -5.011762873823551e-01 -5.011762873738421e-01 8.51297e-12 2.20257e-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 = 1, direction = 2: |F_model - F_numer| error = ----------------------- = 8.26111e-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 = Fe Ti | a0 = 3.8014420753265763 | (Configuration in file "config-FeTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Fe 1 4.301115675776148e-01 4.301115675984180e-01 2.08032e-11 7.62997e-10 2 1.132282887853596e-01 1.132282887807941e-01 4.56549e-12 2.26983e-09 * 3 -1.004539963172183e-01 -1.004539963615325e-01 4.43142e-11 1.58900e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -1.987850409210691e+00 -1.987850409212991e+00 2.30038e-12 1.84668e-10 2 -3.062208293874362e-01 -3.062208294115322e-01 2.40960e-11 2.35292e-10 3 5.820301207778172e-01 5.820301208152633e-01 3.74460e-11 1.40746e-09 ----------------------------------------------------------------------------------------------------- 3 Ti 1 7.902901679263134e-02 7.902901678366750e-02 8.96384e-12 1.61413e-10 2 -1.000826215706664e-01 -1.000826215679920e-01 2.67439e-12 1.60823e-10 3 -1.341511055367141e+00 -1.341511055377629e+00 1.04874e-11 1.60985e-09 ----------------------------------------------------------------------------------------------------- 4 Fe 1 6.227465485376767e-02 6.227465488061035e-02 2.68427e-11 5.26669e-11 2 1.973925377047782e+00 1.973925377017528e+00 3.02536e-11 9.71521e-11 3 -1.550922005202230e+00 -1.550922005198339e+00 3.89067e-12 9.94069e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -5.418010154517292e-01 -5.418010154822911e-01 3.05619e-11 2.18051e-09 * 2 3.591802923874257e-01 3.591802923863550e-01 1.07070e-12 1.32233e-09 3 -8.725660544460290e-01 -8.725660544611599e-01 1.51309e-11 3.54535e-11 ----------------------------------------------------------------------------------------------------- 6 Fe 1 -1.049275236146059e+00 -1.049275236149147e+00 3.08753e-12 1.84202e-10 2 3.124017478290110e-01 3.124017477288962e-01 1.00115e-10 5.19296e-10 3 6.418624483490117e-01 6.418624483352723e-01 1.37395e-11 2.67223e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 1.517648264169966e+00 1.517648264277783e+00 1.07817e-10 1.94513e-10 2 -7.681413809666021e-01 -7.681413809357128e-01 3.08893e-11 3.66187e-10 3 7.937575328540112e-01 7.937575328282743e-01 2.57369e-11 4.85367e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -2.626543353433536e+00 -2.626543353467339e+00 3.38036e-11 2.11116e-09 * 2 -8.643306851129574e-01 -8.643306850378836e-01 7.50738e-11 1.08624e-08 * 3 -2.179279402476538e+00 -2.179279402508745e+00 3.22067e-11 1.88702e-09 * ----------------------------------------------------------------------------------------------------- 9 Fe 1 7.646060620628642e-01 7.646060620544152e-01 8.44902e-12 7.30332e-11 2 -3.527617323749319e-01 -3.527617323848909e-01 9.95903e-12 3.55152e-10 3 4.566081616528684e-01 4.566081616442191e-01 8.64930e-12 1.92401e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -2.037010607996550e+00 -2.037010607994480e+00 2.06990e-12 1.86769e-10 2 1.113353491686619e-01 1.113353491858979e-01 1.72360e-11 9.04622e-11 3 -1.548252486403987e+00 -1.548252486404404e+00 4.16778e-13 1.12700e-10 ----------------------------------------------------------------------------------------------------- 11 Fe 1 4.699126807818755e-01 4.699126808014741e-01 1.95986e-11 3.48348e-10 2 1.950757829836385e-01 1.950757829823868e-01 1.25172e-12 2.17892e-09 * 3 -1.251738679173249e+00 -1.251738679196405e+00 2.31553e-11 6.67710e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 4.493062182302513e-01 4.493062182429200e-01 1.26687e-11 7.04152e-11 2 -4.776464079988728e-01 -4.776464079852036e-01 1.36692e-11 1.41206e-10 3 9.907377679236311e-01 9.907377679239447e-01 3.13638e-13 1.38002e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 2.497457632794162e+00 2.497457632829807e+00 3.56453e-11 3.10691e-10 2 -1.713819129672206e+00 -1.713819129693825e+00 2.16187e-11 1.33624e-10 3 -2.830680961118855e-01 -2.830680961369696e-01 2.50841e-11 1.07102e-10 ----------------------------------------------------------------------------------------------------- 14 Fe 1 3.397675453171391e-01 3.397675453066991e-01 1.04400e-11 3.70115e-12 2 2.529326138274545e-01 2.529326138120335e-01 1.54210e-11 1.41205e-10 3 3.188530751491920e-01 3.188530751697590e-01 2.05669e-11 7.64894e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 1.592338937322121e+00 1.592338937424313e+00 1.02192e-10 4.45100e-10 2 2.394453347765571e+00 2.394453347765456e+00 1.14575e-13 3.09026e-10 3 -2.491764938347960e+00 -2.491764938265975e+00 8.19851e-11 1.76324e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 5.057227909313978e-01 5.057227909300139e-01 1.38389e-12 5.06265e-09 * 2 -2.573743167214175e-01 -2.573743167189502e-01 2.46730e-12 4.37662e-10 3 1.462008391130877e+00 1.462008391084494e+00 4.63833e-11 1.55102e-10 ----------------------------------------------------------------------------------------------------- 17 Fe 1 -2.560630926307499e-01 -2.560630926042627e-01 2.64872e-11 2.48961e-10 2 -8.844861916398785e-01 -8.844861916407266e-01 8.48099e-13 5.38798e-11 3 1.855616143399958e+00 1.855616143336977e+00 6.29810e-11 1.65991e-10 ----------------------------------------------------------------------------------------------------- 18 Fe 1 7.266105653254367e-01 7.266105653252563e-01 1.80411e-13 3.11567e-09 * 2 1.124958558219394e+00 1.124958558154114e+00 6.52802e-11 7.03495e-11 3 2.094986039858752e+00 2.094986039852770e+00 5.98144e-12 1.99502e-10 ----------------------------------------------------------------------------------------------------- 19 Fe 1 -1.068144538907756e+00 -1.068144538903317e+00 4.43823e-12 3.37228e-11 2 9.288428714085400e-01 9.288428713937512e-01 1.47888e-11 1.38895e-10 3 1.910798976413987e-01 1.910798976680803e-01 2.66816e-11 1.63148e-10 ----------------------------------------------------------------------------------------------------- 20 Fe 1 8.051577451344114e-01 8.051577451304561e-01 3.95528e-12 1.07684e-10 2 -4.462872790979384e-01 -4.462872791019494e-01 4.01101e-12 7.20250e-11 3 -6.274035371046881e-01 -6.274035370946662e-01 1.00219e-11 1.38333e-09 ----------------------------------------------------------------------------------------------------- 21 Ti 1 1.075440752216729e+00 1.075440752217219e+00 4.89830e-13 3.60526e-10 2 -3.610001252967264e-01 -3.610001253003552e-01 3.62882e-12 5.40635e-10 3 -3.404835140328738e-02 -3.404835139242268e-02 1.08647e-11 1.05641e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 6.368498840008842e-01 6.368498839533483e-01 4.75359e-11 6.33686e-10 2 -2.051740828063095e-01 -2.051740828233513e-01 1.70418e-11 1.63897e-10 3 1.608389474163394e+00 1.608389474178409e+00 1.50144e-11 1.04660e-10 ----------------------------------------------------------------------------------------------------- 23 Fe 1 -3.943530524319641e-01 -3.943530523851994e-01 4.67647e-11 2.26822e-10 2 -7.615581746130509e-01 -7.615581746143195e-01 1.26865e-12 1.86738e-10 3 8.106758555701431e-01 8.106758554882953e-01 8.18478e-11 2.14998e-09 * ----------------------------------------------------------------------------------------------------- 24 Fe 1 4.981468323105583e-01 4.981468323052286e-01 5.32968e-12 1.77801e-10 2 -4.613991093342765e-01 -4.613991092627738e-01 7.15027e-11 1.39312e-10 3 -4.501564547734737e-01 -4.501564546780997e-01 9.53740e-11 7.12597e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 3.742122288407166e-01 3.742122288728834e-01 3.21668e-11 1.34391e-10 2 -4.896438952761921e-01 -4.896438952820291e-01 5.83700e-12 1.63709e-10 3 6.617609010466561e-01 6.617609010258941e-01 2.07619e-11 3.23487e-10 ----------------------------------------------------------------------------------------------------- 26 Fe 1 -9.611874285260139e-01 -9.611874285220409e-01 3.97304e-12 4.50832e-11 2 -4.718971751121426e-01 -4.718971751274219e-01 1.52793e-11 3.43740e-09 * 3 2.658022731392089e-01 2.658022731254518e-01 1.37571e-11 3.26118e-10 ----------------------------------------------------------------------------------------------------- 27 Fe 1 -4.711247518417315e-01 -4.711247518702936e-01 2.85620e-11 2.50886e-10 2 4.567097410014689e-01 4.567097410789565e-01 7.74876e-11 1.30876e-10 3 -1.080157687834023e+00 -1.080157687858168e+00 2.41447e-11 9.26785e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 8.853349244641283e-01 8.853349244808874e-01 1.67590e-11 7.11585e-11 2 -5.056861545712801e-01 -5.056861545188629e-01 5.24172e-11 1.32472e-10 3 -2.780139814319192e-01 -2.780139814175879e-01 1.43314e-11 9.79715e-11 ----------------------------------------------------------------------------------------------------- 29 Fe 1 -1.864857806393812e+00 -1.864857806371136e+00 2.26761e-11 8.82963e-11 2 1.652671914100908e+00 1.652671914056849e+00 4.40588e-11 2.45093e-09 * 3 1.126008484468329e+00 1.126008484365476e+00 1.02853e-10 8.73283e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 7.477419987868035e-01 7.477419987902671e-01 3.46367e-12 5.87334e-11 2 2.025194619669263e+00 2.025194619666612e+00 2.65121e-12 2.00646e-10 3 -2.732496526267281e+00 -2.732496526365745e+00 9.84639e-11 2.27293e-09 * ----------------------------------------------------------------------------------------------------- 31 Fe 1 5.050212479908576e-01 5.050212480359573e-01 4.50997e-11 1.65362e-10 2 -2.638916888744394e+00 -2.638916888780880e+00 3.64868e-11 7.10512e-11 3 2.081433433694969e+00 2.081433433699518e+00 4.54925e-12 2.03267e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -1.704480256933725e+00 -1.704480257072422e+00 1.38696e-10 4.26047e-10 2 1.655156761028004e-01 1.655156761000375e-01 2.76290e-12 2.45391e-10 3 8.802232518406911e-01 8.802232518548945e-01 1.42034e-11 1.12718e-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 = 1, direction = 3: |F_model - F_numer| error = ----------------------- = 4.41140e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 1.27838e-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 1.27838e-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.