!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_KavousiNovakBaskes_2019_NiTi__MO_050461957184_002 Supported species : Ni 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 = Ni | a0 = 3.5213918685913086 | (Configuration in file "config-Ni.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ni 1 1.030386549206983e-01 1.030386549175129e-01 3.18547e-12 5.06859e-10 2 -3.574187105685731e-01 -3.574187105643860e-01 4.18710e-12 6.13309e-11 3 -8.495590986514721e-01 -8.495590986107484e-01 4.07236e-11 6.70627e-11 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -1.050146370891780e+00 -1.050146370864431e+00 2.73490e-11 3.42281e-10 2 7.506510428890971e-01 7.506510429121893e-01 2.30922e-11 1.22429e-10 3 1.038947415035456e+00 1.038947415030145e+00 5.31175e-12 3.85840e-11 ----------------------------------------------------------------------------------------------------- 3 Ni 1 2.126044256880591e+00 2.126044256850949e+00 2.96421e-11 3.71588e-10 2 6.596506387430775e-01 6.596506387322423e-01 1.08352e-11 7.16357e-10 3 -1.416409043066893e+00 -1.416409043054634e+00 1.22589e-11 2.24585e-11 ----------------------------------------------------------------------------------------------------- 4 Ni 1 1.011374530063913e+00 1.011374530088037e+00 2.41238e-11 7.61124e-11 2 6.392609512594613e-01 6.392609512547962e-01 4.66505e-12 9.21914e-10 3 9.822830988264691e-01 9.822830988194309e-01 7.03826e-12 7.59679e-11 ----------------------------------------------------------------------------------------------------- 5 Ni 1 5.062413671205885e-01 5.062413671092910e-01 1.12975e-11 1.15004e-10 2 -7.152690540927731e-02 -7.152690539371086e-02 1.55665e-11 2.21599e-09 * 3 6.577906412135176e-01 6.577906412078091e-01 5.70854e-12 1.74509e-11 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -7.615667189743602e-01 -7.615667189994780e-01 2.51178e-11 1.85374e-10 2 4.262434129794790e-01 4.262434129744899e-01 4.98906e-12 1.84256e-10 3 7.049169864272531e-01 7.049169864303804e-01 3.12728e-12 5.43309e-11 ----------------------------------------------------------------------------------------------------- 7 Ni 1 4.973885498814168e-01 4.973885499021009e-01 2.06841e-11 1.34830e-10 2 -3.260972505999356e+00 -3.260972506007811e+00 8.45501e-12 3.01816e-11 3 -4.026638793619425e+00 -4.026638793667431e+00 4.80052e-11 1.67658e-10 ----------------------------------------------------------------------------------------------------- 8 Ni 1 -2.102715639951064e+00 -2.102715639903541e+00 4.75233e-11 2.61066e-10 2 -2.037901010110620e+00 -2.037901010152978e+00 4.23581e-11 3.16808e-10 3 -1.080347018122317e+00 -1.080347018101745e+00 2.05718e-11 3.99933e-10 ----------------------------------------------------------------------------------------------------- 9 Ni 1 -8.143885327846052e-01 -8.143885327207318e-01 6.38735e-11 1.70464e-10 2 -2.532272556943150e+00 -2.532272556858286e+00 8.48646e-11 2.40838e-10 3 -3.499123674822221e+00 -3.499123674774392e+00 4.78293e-11 1.37641e-10 ----------------------------------------------------------------------------------------------------- 10 Ni 1 -1.276823671944013e+00 -1.276823671948006e+00 3.99303e-12 5.02569e-11 2 1.036403373995746e+00 1.036403373988544e+00 7.20224e-12 5.02638e-11 3 -1.558068106044454e+00 -1.558068106026134e+00 1.83198e-11 1.14619e-10 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -2.528707835973679e-01 -2.528707836588972e-01 6.15293e-11 2.65472e-10 2 -1.661116782979103e+00 -1.661116782997216e+00 1.81133e-11 7.63849e-10 3 2.594556576271417e+00 2.594556576267944e+00 3.47278e-12 1.19549e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 7.542268773588255e-03 7.542268754775468e-03 1.88128e-11 4.29696e-10 2 2.541703345218906e+00 2.541703345215187e+00 3.71880e-12 1.62732e-10 3 2.107165696585548e+00 2.107165696575355e+00 1.01923e-11 1.04452e-08 * ----------------------------------------------------------------------------------------------------- 13 Ni 1 -1.481735453537661e+00 -1.481735453569550e+00 3.18889e-11 2.57871e-10 2 -2.287737916674467e+00 -2.287737916703076e+00 2.86087e-11 6.30673e-10 3 -4.606220452438235e+00 -4.606220452456202e+00 1.79670e-11 1.32523e-10 ----------------------------------------------------------------------------------------------------- 14 Ni 1 4.462911675187389e-01 4.462911675187511e-01 1.22680e-14 3.15610e-11 2 1.060526567659265e+00 1.060526567666687e+00 7.42162e-12 1.58190e-10 3 -5.363226492725969e-01 -5.363226492722014e-01 3.95461e-13 1.00670e-10 ----------------------------------------------------------------------------------------------------- 15 Ni 1 4.025991634624911e+00 4.025991634668745e+00 4.38343e-11 5.25340e-11 2 -1.206890421041652e+00 -1.206890421008888e+00 3.27640e-11 5.68974e-11 3 1.621865272717136e+00 1.621865272729922e+00 1.27860e-11 2.22026e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 1.229748970522312e+00 1.229748970509086e+00 1.32254e-11 2.00526e-10 2 2.929819808796820e+00 2.929819808794344e+00 2.47669e-12 7.56897e-11 3 1.603833485104995e+00 1.603833485047409e+00 5.75862e-11 6.68472e-11 ----------------------------------------------------------------------------------------------------- 17 Ni 1 -2.005082658291240e+00 -2.005082658262167e+00 2.90732e-11 1.42313e-09 * 2 2.942704911818075e-01 2.942704911504574e-01 3.13501e-11 5.41885e-11 3 4.864355075333596e-01 4.864355075087909e-01 2.45687e-11 3.18562e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 4.312531006715554e-01 4.312531006483026e-01 2.32528e-11 2.15958e-10 2 2.087873043295422e+00 2.087873043279047e+00 1.63753e-11 4.81577e-10 3 -1.521143619326996e+00 -1.521143619298276e+00 2.87195e-11 1.05184e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 1.285319567211197e+00 1.285319567198915e+00 1.22815e-11 3.18902e-10 2 -9.243371280151811e-01 -9.243371278840760e-01 1.31105e-10 1.71880e-10 3 1.562790863145508e+00 1.562790863135807e+00 9.70068e-12 7.15764e-10 ----------------------------------------------------------------------------------------------------- 20 Ni 1 3.975745900067116e-01 3.975745900355764e-01 2.88649e-11 1.04287e-10 2 5.299522744400711e-01 5.299522744230972e-01 1.69739e-11 8.56573e-09 * 3 -5.194808166089290e-01 -5.194808165924808e-01 1.64482e-11 1.76701e-09 * ----------------------------------------------------------------------------------------------------- 21 Ni 1 -1.719396003459187e+00 -1.719396003465757e+00 6.57030e-12 1.00627e-10 2 1.713373022226554e-01 1.713373022049010e-01 1.77545e-11 1.17423e-11 3 9.967398956633386e-01 9.967398957931033e-01 1.29765e-10 5.52683e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 4.955341784045757e-01 4.955341784113288e-01 6.75310e-12 2.26355e-10 2 3.383813628151055e+00 3.383813628129478e+00 2.15770e-11 3.21801e-10 3 3.761981968305499e+00 3.761981968313652e+00 8.15259e-12 1.40651e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 4.209963617437315e-01 4.209963617352642e-01 8.46728e-12 5.89792e-11 2 -2.434749610298718e-02 -2.434749612442432e-02 2.14371e-11 9.20700e-11 3 -2.713167037920020e-01 -2.713167037760492e-01 1.59529e-11 8.37957e-12 ----------------------------------------------------------------------------------------------------- 24 Ni 1 -5.070210450275070e-01 -5.070210449898849e-01 3.76221e-11 3.64909e-10 2 7.648439071139544e-01 7.648439071007449e-01 1.32095e-11 2.68671e-10 3 -8.475863684302858e-01 -8.475863684527399e-01 2.24541e-11 9.76265e-11 ----------------------------------------------------------------------------------------------------- 25 Ni 1 -2.806204531903431e-01 -2.806204531908932e-01 5.50060e-13 1.79346e-10 2 -1.342668715551101e+00 -1.342668715533337e+00 1.77636e-11 2.48742e-09 * 3 4.056687190583685e-01 4.056687190515655e-01 6.80306e-12 8.62691e-10 ----------------------------------------------------------------------------------------------------- 26 Ni 1 -1.214591399495819e+00 -1.214591399492661e+00 3.15725e-12 3.20485e-10 2 8.541988004921499e-01 8.541988004813631e-01 1.07868e-11 1.28906e-10 3 -1.174970221649705e+00 -1.174970221642355e+00 7.34945e-12 7.55547e-11 ----------------------------------------------------------------------------------------------------- 27 Ni 1 1.860568657382499e+00 1.860568657385224e+00 2.72449e-12 2.93451e-10 2 -4.334559874436911e+00 -4.334559874380052e+00 5.68585e-11 4.35793e-10 3 2.346558344409869e-01 2.346558344728991e-01 3.19122e-11 2.97644e-09 * ----------------------------------------------------------------------------------------------------- 28 Ni 1 -2.518524689744116e+00 -2.518524689752536e+00 8.42038e-12 1.10081e-10 2 2.416609153541848e+00 2.416609153513973e+00 2.78750e-11 1.85655e-10 3 -2.169864387214113e-01 -2.169864387265469e-01 5.13567e-12 2.13571e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 -1.122034824614194e+00 -1.122034824577092e+00 3.71017e-11 1.19428e-10 2 -1.191048516816883e+00 -1.191048516845319e+00 2.84364e-11 3.59588e-10 3 1.465423410085013e+00 1.465423410103089e+00 1.80755e-11 3.81397e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 5.421958819325107e-02 5.421958811968036e-02 7.35707e-11 1.07146e-10 2 8.563477369802891e-01 8.563477369649961e-01 1.52930e-11 2.10769e-10 3 9.215909725871361e-01 9.215909726166472e-01 2.95112e-11 9.79092e-11 ----------------------------------------------------------------------------------------------------- 31 Ni 1 9.723812501049820e-01 9.723812501137090e-01 8.72702e-12 7.40135e-11 2 -1.078205189946503e+00 -1.078205189936972e+00 9.53149e-12 1.62608e-10 3 5.060649452505290e-01 5.060649452440381e-01 6.49092e-12 2.62866e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.236009551477995e+00 1.236009551453219e+00 2.47760e-11 2.47544e-10 2 9.074982516346604e-01 9.074982516368457e-01 2.18536e-12 6.93483e-11 3 4.714617163154109e-01 4.714617162555247e-01 5.98862e-11 2.54171e-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 = 12, direction = 1: |F_model - F_numer| error = ----------------------- = 2.49431e-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 = 4.1169843673706055 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 6.527398374266702e-01 6.527398374298152e-01 3.14504e-12 2.72414e-11 2 5.430295790685866e-01 5.430295790617031e-01 6.88349e-12 5.23304e-11 3 8.547187299026275e-01 8.547187299053136e-01 2.68607e-12 3.50243e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -9.667295427694244e-01 -9.667295427266975e-01 4.27268e-11 9.92511e-11 2 9.474784189903837e-01 9.474784190670302e-01 7.66466e-11 9.14935e-11 3 -1.132668041166899e+00 -1.132668041172439e+00 5.54023e-12 2.45191e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.699252573949039e+00 -1.699252573979688e+00 3.06495e-11 4.32006e-10 2 -9.221842678210881e-01 -9.221842678468550e-01 2.57669e-11 7.14786e-09 * 3 -2.192540116790222e-01 -2.192540117183495e-01 3.93273e-11 4.79871e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 5.843655336997411e-01 5.843655336934394e-01 6.30174e-12 7.73079e-11 2 5.965004490197717e-02 5.965004490825702e-02 6.27984e-12 9.39366e-10 3 7.232173927566610e-01 7.232173927040497e-01 5.26112e-11 1.89635e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.366083285254588e-01 -2.366083285201246e-01 5.33418e-12 7.47595e-11 2 -7.252367965628517e-02 -7.252367964370895e-02 1.25762e-11 7.83680e-11 3 1.248396187186931e-01 1.248396186870344e-01 3.16587e-11 1.40167e-09 ----------------------------------------------------------------------------------------------------- 6 Ti 1 9.704357729830727e-02 9.704357729855660e-02 2.49328e-13 5.13298e-10 2 -4.196053959729911e-02 -4.196053960186926e-02 4.57015e-12 5.12837e-11 3 1.016373165440305e-01 1.016373165448848e-01 8.54261e-13 2.15257e-09 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -6.247844233402735e-01 -6.247844233457870e-01 5.51348e-12 1.78404e-10 2 -3.849580579459176e-02 -3.849580579443185e-02 1.59914e-13 1.48772e-09 3 1.855982696651431e-01 1.855982696691664e-01 4.02328e-12 1.64034e-09 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.508297002120723e+00 1.508297002065290e+00 5.54332e-11 4.59639e-10 2 1.917833650167306e+00 1.917833650169707e+00 2.40075e-12 1.75713e-10 3 1.463684934399078e+00 1.463684934372421e+00 2.66569e-11 8.71365e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -2.961403025593950e-01 -2.961403025519709e-01 7.42406e-12 8.84430e-11 2 -7.429802193324659e-01 -7.429802193274311e-01 5.03486e-12 3.25948e-11 3 -1.348538876063481e+00 -1.348538876088961e+00 2.54798e-11 1.48261e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -4.277244242056947e-01 -4.277244241836735e-01 2.20212e-11 7.73156e-11 2 1.757023518399450e+00 1.757023518398750e+00 6.99441e-13 8.40044e-11 3 -1.037652859295609e+00 -1.037652859306040e+00 1.04312e-11 5.61768e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 1.614265627776611e+00 1.614265627825664e+00 4.90532e-11 1.15751e-10 2 -2.032957241278362e+00 -2.032957241286294e+00 7.93188e-12 1.93743e-10 3 2.979806689903293e+00 2.979806689902952e+00 3.40172e-13 2.22466e-09 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -5.037941391232593e-01 -5.037941391272817e-01 4.02234e-12 1.00851e-10 2 1.115722598743622e+00 1.115722598734118e+00 9.50395e-12 1.59483e-10 3 1.560044582887414e+00 1.560044582900446e+00 1.30320e-11 1.61424e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.265458530471868e+00 1.265458530492104e+00 2.02360e-11 9.10179e-11 2 -5.720016329006876e-01 -5.720016328972798e-01 3.40783e-12 5.44340e-10 3 -1.448441072373224e-01 -1.448441072079589e-01 2.93635e-11 1.04425e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -7.029535435623325e-01 -7.029535435769516e-01 1.46191e-11 8.15620e-11 2 -4.812868368261607e-01 -4.812868368736727e-01 4.75119e-11 1.94383e-10 3 1.840584193764408e-01 1.840584193898457e-01 1.34049e-11 9.82422e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -5.485145419679035e-01 -5.485145419428439e-01 2.50596e-11 8.57983e-11 2 -1.302276164593061e+00 -1.302276164516849e+00 7.62117e-11 2.06654e-09 3 4.342291131943192e-01 4.342291131699209e-01 2.43983e-11 6.40687e-11 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.077237848410424e+00 -1.077237848428895e+00 1.84712e-11 1.42102e-09 2 -2.055287464398690e-01 -2.055287464384383e-01 1.43069e-12 5.23691e-09 * 3 -1.229735149571128e-01 -1.229735149557737e-01 1.33907e-12 1.10947e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 7.719996907139076e-03 7.719996866568522e-03 4.05706e-11 5.66082e-11 2 -6.628372974903890e-01 -6.628372974869247e-01 3.46434e-12 4.07672e-10 3 -5.043025073796855e-01 -5.043025073752495e-01 4.43601e-12 9.49435e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 1.525284588609273e+00 1.525284588645808e+00 3.65346e-11 3.41017e-10 2 3.320691333022126e-01 3.320691332684359e-01 3.37767e-11 1.50059e-09 3 -1.816146469343234e+00 -1.816146469346881e+00 3.64642e-12 1.96427e-09 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -5.655759037979985e-01 -5.655759038314714e-01 3.34729e-11 1.85439e-10 2 4.576860081335662e-01 4.576860081487956e-01 1.52294e-11 2.50178e-09 3 7.745805691234264e-01 7.745805691266482e-01 3.22176e-12 1.31498e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.029317862083410e+00 -1.029317862093138e+00 9.72777e-12 1.94843e-10 2 -5.947067811215625e-01 -5.947067811615953e-01 4.00328e-11 6.85461e-11 3 8.740866231524324e-01 8.740866231432052e-01 9.22717e-12 1.03229e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 5.973662500971935e-01 5.973662500536869e-01 4.35065e-11 2.36390e-10 2 -9.410559884213346e-01 -9.410559883767170e-01 4.46176e-11 9.62647e-11 3 3.320485930622987e-01 3.320485930307269e-01 3.15718e-11 1.21749e-09 ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.309070818894081e+00 1.309070818992312e+00 9.82310e-11 1.26823e-09 2 2.028265642595165e+00 2.028265642602242e+00 7.07701e-12 2.55441e-10 3 4.898376762406870e-01 4.898376762542465e-01 1.35594e-11 3.08848e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -9.287403414580504e-01 -9.287403414430018e-01 1.50486e-11 9.26326e-10 2 8.376390960929549e-01 8.376390960936209e-01 6.65912e-13 1.57433e-10 3 -8.660090183051998e-01 -8.660090183043631e-01 8.36775e-13 1.89590e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.289875017369488e+00 -1.289875017305120e+00 6.43685e-11 1.10767e-10 2 -1.386994062574681e+00 -1.386994062579654e+00 4.97291e-12 4.98304e-09 * 3 -7.088372519529168e-01 -7.088372519797000e-01 2.67832e-11 4.07579e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.049960263444435e+00 -1.049960263450993e+00 6.55831e-12 1.63699e-09 2 -1.304973199505282e+00 -1.304973199514319e+00 9.03744e-12 1.98190e-10 3 -3.469859529855925e+00 -3.469859529840249e+00 1.56763e-11 1.77505e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 1.189837543626611e+00 1.189837543604775e+00 2.18365e-11 2.47219e-10 2 2.425190897363710e-02 2.425190901777785e-02 4.41407e-11 1.87992e-10 3 -3.510579792690101e+00 -3.510579792674153e+00 1.59477e-11 1.85774e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 3.996786837510813e+00 3.996786837536858e+00 2.60449e-11 1.12884e-10 2 -5.034170823591165e-01 -5.034170823568684e-01 2.24809e-12 8.58319e-10 3 1.394045567823264e+00 1.394045567837358e+00 1.40947e-11 4.85534e-11 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -1.931885997848003e+00 -1.931885997817614e+00 3.03895e-11 3.17462e-11 2 1.939734658437257e+00 1.939734658410984e+00 2.62728e-11 1.80818e-10 3 2.055567923385084e+00 2.055567923391860e+00 6.77591e-12 1.18886e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -9.734500295149924e-01 -9.734500295276680e-01 1.26756e-11 1.43598e-09 2 6.245220731644181e-01 6.245220731736293e-01 9.21119e-12 2.66831e-10 3 4.692800393453733e-01 4.692800393274035e-01 1.79698e-11 1.65698e-09 ----------------------------------------------------------------------------------------------------- 30 Ti 1 4.474406939686663e-01 4.474406939927380e-01 2.40717e-11 2.43422e-10 2 6.055440779668079e-01 6.055440779771946e-01 1.03867e-11 3.78142e-10 3 -1.250080190848967e+00 -1.250080190843193e+00 5.77360e-12 1.66906e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 5.082449121328265e-01 5.082449121431155e-01 1.02890e-11 1.57971e-09 2 -7.868870980007976e-01 -7.868870979793868e-01 2.14108e-11 1.92747e-10 3 4.632707891159226e-01 4.632707891178933e-01 1.97065e-12 8.97066e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -4.513766666109433e-01 -4.513766666099081e-01 1.03523e-12 4.35565e-11 2 -5.973837652243081e-01 -5.973837652096921e-01 1.46161e-11 9.52654e-11 3 6.671933221792831e-01 6.671933221530445e-01 2.62386e-11 2.59322e-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 = 17, direction = 1: |F_model - F_numer| error = ----------------------- = 5.25526e-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. MIXED STRUCTURE -- Species = Ni Ti | a0 = 3.820660320126808 | (Configuration in file "config-NiTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 8.838151525817707e-01 8.838151525827077e-01 9.37028e-13 4.06452e-10 2 5.893687025942497e-01 5.893687025963918e-01 2.14218e-12 2.52613e-11 3 -1.520046180531092e-01 -1.520046180595525e-01 6.44337e-12 5.71723e-10 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -1.263405625671584e+00 -1.263405625539551e+00 1.32033e-10 2.67987e-10 2 -1.274639802414578e+00 -1.274639802411803e+00 2.77578e-12 3.58723e-10 3 1.160199545906072e+00 1.160199545923946e+00 1.78748e-11 7.02455e-10 ----------------------------------------------------------------------------------------------------- 3 Ni 1 6.634719462920441e-01 6.634719462928692e-01 8.25118e-13 7.77900e-11 2 -3.144045840328843e-01 -3.144045840322168e-01 6.67577e-13 2.58409e-10 3 -3.366731552333211e-01 -3.366731552229801e-01 1.03410e-11 1.63402e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 1.118727329272745e+00 1.118727329254487e+00 1.82578e-11 3.99292e-11 2 -3.935052633608275e+00 -3.935052633620707e+00 1.24327e-11 1.07896e-10 3 -1.100326248707049e+00 -1.100326248699895e+00 7.15472e-12 1.42750e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -1.326363624040317e+00 -1.326363624075003e+00 3.46865e-11 1.68779e-10 2 4.322299584288852e-01 4.322299584518849e-01 2.29997e-11 5.06947e-11 3 -1.421313819594814e-01 -1.421313819454234e-01 1.40580e-11 4.20718e-11 ----------------------------------------------------------------------------------------------------- 6 Ni 1 1.553373594970380e+00 1.553373594970268e+00 1.12133e-13 2.17586e-11 2 1.847567560093200e+00 1.847567560095636e+00 2.43650e-12 1.00697e-10 3 -1.738609390639726e+00 -1.738609390645959e+00 6.23390e-12 2.33523e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -3.440334259884406e+00 -3.440334259899215e+00 1.48099e-11 1.25152e-09 2 -4.388583521393659e+00 -4.388583521423929e+00 3.02700e-11 1.47144e-10 3 1.623863346338509e+00 1.623863346328009e+00 1.04996e-11 3.51589e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -6.991097407508281e+00 -6.991097407488903e+00 1.93783e-11 6.48950e-09 * 2 -3.651906909009926e+00 -3.651906908988278e+00 2.16480e-11 3.45256e-10 3 2.937994940901718e+00 2.937994940961318e+00 5.95999e-11 1.49287e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 3.806790171790535e+00 3.806790171786711e+00 3.82405e-12 1.23319e-10 2 -2.059924279211204e+00 -2.059924279230411e+00 1.92069e-11 2.43709e-10 3 -1.192112728720338e+00 -1.192112728728941e+00 8.60290e-12 1.15992e-11 ----------------------------------------------------------------------------------------------------- 10 Ni 1 -2.526968711356154e+00 -2.526968711370024e+00 1.38702e-11 5.05330e-10 2 -6.183913077295627e-02 -6.183913077702258e-02 4.06631e-12 1.09042e-10 3 -1.530971777723654e+00 -1.530971777748688e+00 2.50344e-11 3.69851e-10 ----------------------------------------------------------------------------------------------------- 11 Ni 1 6.824239089486267e-02 6.824239092974083e-02 3.48782e-11 5.48406e-10 2 -2.708165464366652e+00 -2.708165464355932e+00 1.07203e-11 1.08094e-08 * 3 -2.814613022352395e+00 -2.814613022332928e+00 1.94671e-11 1.41073e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 -1.837678090056894e+00 -1.837678090056056e+00 8.37774e-13 9.82534e-10 2 6.717145325511911e+00 6.717145325475667e+00 3.62439e-11 3.67315e-10 3 2.215376018012892e+00 2.215376018083045e+00 7.01532e-11 7.03806e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -1.389798833261096e-01 -1.389798833126173e-01 1.34923e-11 3.74007e-10 2 7.759356983018590e-01 7.759356982635202e-01 3.83389e-11 3.29976e-10 3 -8.470515963504907e-01 -8.470515962677807e-01 8.27100e-11 2.32665e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -2.313559316488059e-01 -2.313559316830871e-01 3.42813e-11 9.48200e-11 2 -2.477908499708986e+00 -2.477908499705801e+00 3.18456e-12 2.02740e-11 3 -1.912763783213503e+00 -1.912763783203942e+00 9.56057e-12 1.15553e-09 ----------------------------------------------------------------------------------------------------- 15 Ni 1 1.093036558418017e+00 1.093036558430276e+00 1.22595e-11 1.64966e-10 2 1.248875382654191e+00 1.248875382646269e+00 7.92233e-12 4.62353e-10 3 1.800995641808863e+00 1.800995641745101e+00 6.37623e-11 5.17781e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 3.094424578324388e+00 3.094424578214082e+00 1.10306e-10 2.49273e-10 2 -2.629931402306858e-01 -2.629931402342822e-01 3.59640e-12 4.90050e-11 3 3.574947375380994e+00 3.574947375524333e+00 1.43339e-10 9.46985e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 1.220485450360840e+00 1.220485450365031e+00 4.19043e-12 9.22877e-11 2 9.936349208353320e-01 9.936349208169033e-01 1.84287e-11 8.54856e-11 3 1.715821730168317e-01 1.715821730172716e-01 4.39870e-13 1.00482e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 -3.513846843196242e-01 -3.513846843408012e-01 2.11769e-11 5.18200e-11 2 7.934708327582733e-01 7.934708328202030e-01 6.19297e-11 8.24013e-11 3 -2.146668179693053e-02 -2.146668180946579e-02 1.25353e-11 2.33335e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 -6.177599200170270e-02 -6.177599199963963e-02 2.06306e-12 4.04674e-11 2 1.093618997918711e+00 1.093618997884836e+00 3.38747e-11 1.18754e-10 3 -8.818855711473637e-01 -8.818855711372710e-01 1.00927e-11 4.37509e-11 ----------------------------------------------------------------------------------------------------- 20 Ni 1 -3.967597335173161e-01 -3.967597335241075e-01 6.79135e-12 1.10350e-10 2 -7.526334636205608e-01 -7.526334636549392e-01 3.43784e-11 3.75019e-11 3 -7.193571278397785e-01 -7.193571278371523e-01 2.62612e-12 3.92528e-10 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -2.208908645421457e+00 -2.208908645438168e+00 1.67106e-11 1.40871e-10 2 -1.657563908166854e+00 -1.657563908182029e+00 1.51759e-11 1.21625e-08 * 3 -9.915472413886279e+00 -9.915472413767944e+00 1.18336e-10 1.04402e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 8.271789684676918e+00 8.271789684647942e+00 2.89759e-11 2.01971e-08 * 2 9.534187419478517e+00 9.534187419432937e+00 4.55795e-11 3.72118e-10 3 8.143456529842233e+00 8.143456530001204e+00 1.58972e-10 3.74245e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 5.341980592113020e-01 5.341980592123344e-01 1.03240e-12 8.21965e-11 2 3.891687741078582e-01 3.891687740673533e-01 4.05049e-11 3.94730e-10 3 -3.590120422635090e-01 -3.590120423135897e-01 5.00807e-11 2.16541e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -4.060551397272149e-01 -4.060551397469045e-01 1.96896e-11 6.94209e-10 2 -1.594396929447931e+00 -1.594396929427205e+00 2.07252e-11 1.18321e-10 3 -5.344376140417940e-01 -5.344376140780998e-01 3.63057e-11 1.00839e-09 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -8.341386173457146e-01 -8.341386172554839e-01 9.02307e-11 7.80456e-11 2 4.886751335750932e-01 4.886751335777072e-01 2.61396e-12 2.50755e-10 3 4.054705799666269e+00 4.054705799661154e+00 5.11502e-12 3.57299e-09 * ----------------------------------------------------------------------------------------------------- 26 Ti 1 7.391679264575883e-01 7.391679264576565e-01 6.81677e-14 2.18702e-09 * 2 1.834254447056690e+00 1.834254447021233e+00 3.54572e-11 1.07570e-10 3 -3.013259254604764e+00 -3.013259254559143e+00 4.56204e-11 1.12849e-09 ----------------------------------------------------------------------------------------------------- 27 Ti 1 3.040360911008413e+00 3.040360910981288e+00 2.71250e-11 7.44615e-10 2 -2.826618859583812e+00 -2.826618859591372e+00 7.55973e-12 1.14151e-10 3 1.199460250973278e+00 1.199460250964373e+00 8.90421e-12 3.30079e-09 * ----------------------------------------------------------------------------------------------------- 28 Ti 1 -2.241278693402642e+00 -2.241278693409278e+00 6.63558e-12 1.11491e-10 2 1.147159275215330e+00 1.147159275216562e+00 1.23190e-12 6.40445e-11 3 8.731527937591851e-01 8.731527937847512e-01 2.55661e-11 9.20700e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 -8.081603768562443e+00 -8.081603768594135e+00 3.16920e-11 4.52022e-10 2 -3.102171386515062e+00 -3.102171386398985e+00 1.16076e-10 5.46055e-10 3 -3.399831194442591e+00 -3.399831194478657e+00 3.60658e-11 6.10965e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 2.721766177929751e+00 2.721766177852760e+00 7.69909e-11 6.36844e-10 2 -1.799090787834973e+00 -1.799090787841023e+00 6.05005e-12 6.16004e-10 3 5.843512898270020e+00 5.843512898270206e+00 1.86517e-13 2.74622e-09 * ----------------------------------------------------------------------------------------------------- 31 Ti 1 3.400321118795637e+00 3.400321118835425e+00 3.97882e-11 9.14455e-11 2 5.821702724694950e+00 5.821702724724288e+00 2.93383e-11 3.41513e-11 3 -2.334701082651225e+00 -2.334701082669563e+00 1.83378e-11 1.52243e-09 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.281177568054763e-01 1.281177567928120e-01 1.26644e-11 1.21412e-10 2 -8.391018533060475e-01 -8.391018532984650e-01 7.58249e-12 2.36280e-09 * 3 -6.525666282495571e-01 -6.525666282756092e-01 2.60520e-11 8.40037e-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 = 18, direction = 3: |F_model - F_numer| error = ----------------------- = 5.83940e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 5.25526e-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 5.25526e-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.