!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_000 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 1.030386549175128e-01 3.18554e-12 5.06859e-10 2 -3.574187105685731e-01 -3.574187105643857e-01 4.18737e-12 6.13309e-11 3 -8.495590986514721e-01 -8.495590986107476e-01 4.07244e-11 6.70629e-11 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -1.050146370891780e+00 -1.050146370864430e+00 2.73499e-11 3.42281e-10 2 7.506510428890971e-01 7.506510429121886e-01 2.30915e-11 1.22429e-10 3 1.038947415035456e+00 1.038947415030143e+00 5.31286e-12 3.85845e-11 ----------------------------------------------------------------------------------------------------- 3 Ni 1 2.126044256880591e+00 2.126044256850947e+00 2.96438e-11 3.71590e-10 2 6.596506387430775e-01 6.596506387322417e-01 1.08358e-11 7.16356e-10 3 -1.416409043066893e+00 -1.416409043054633e+00 1.22602e-11 2.24585e-11 ----------------------------------------------------------------------------------------------------- 4 Ni 1 1.011374530063913e+00 1.011374530088036e+00 2.41229e-11 7.61140e-11 2 6.392609512594613e-01 6.392609512547958e-01 4.66549e-12 9.21914e-10 3 9.822830988264691e-01 9.822830988194302e-01 7.03892e-12 7.59683e-11 ----------------------------------------------------------------------------------------------------- 5 Ni 1 5.062413671205885e-01 5.062413671092907e-01 1.12979e-11 1.15005e-10 2 -7.152690540927731e-02 -7.152690539371087e-02 1.55664e-11 2.21599e-09 * 3 6.577906412135176e-01 6.577906412078085e-01 5.70910e-12 1.74504e-11 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -7.615667189743602e-01 -7.615667189994774e-01 2.51171e-11 1.85374e-10 2 4.262434129794790e-01 4.262434129744896e-01 4.98934e-12 1.84256e-10 3 7.049169864272531e-01 7.049169864303797e-01 3.12661e-12 5.43311e-11 ----------------------------------------------------------------------------------------------------- 7 Ni 1 4.973885498814168e-01 4.973885499021005e-01 2.06837e-11 1.34830e-10 2 -3.260972505999356e+00 -3.260972506007808e+00 8.45191e-12 3.01816e-11 3 -4.026638793619425e+00 -4.026638793667426e+00 4.80007e-11 1.67656e-10 ----------------------------------------------------------------------------------------------------- 8 Ni 1 -2.102715639951064e+00 -2.102715639903539e+00 4.75251e-11 2.61068e-10 2 -2.037901010110620e+00 -2.037901010152976e+00 4.23563e-11 3.16807e-10 3 -1.080347018122317e+00 -1.080347018101744e+00 2.05729e-11 3.99933e-10 ----------------------------------------------------------------------------------------------------- 9 Ni 1 -8.143885327846052e-01 -8.143885327207310e-01 6.38742e-11 1.70463e-10 2 -2.532272556943150e+00 -2.532272556858284e+00 8.48659e-11 2.40836e-10 3 -3.499123674822221e+00 -3.499123674774389e+00 4.78324e-11 1.37641e-10 ----------------------------------------------------------------------------------------------------- 10 Ni 1 -1.276823671944013e+00 -1.276823671948006e+00 3.99303e-12 5.02580e-11 2 1.036403373995746e+00 1.036403373988543e+00 7.20335e-12 5.02629e-11 3 -1.558068106044454e+00 -1.558068106026133e+00 1.83209e-11 1.14620e-10 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -2.528707835973679e-01 -2.528707836588970e-01 6.15291e-11 2.65472e-10 2 -1.661116782979103e+00 -1.661116782997215e+00 1.81117e-11 7.63849e-10 3 2.594556576271417e+00 2.594556576267942e+00 3.47544e-12 1.19551e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 7.542268773588255e-03 7.542268754775461e-03 1.88128e-11 4.29696e-10 2 2.541703345218906e+00 2.541703345215185e+00 3.72102e-12 1.62731e-10 3 2.107165696585548e+00 2.107165696575356e+00 1.01914e-11 1.04452e-08 * ----------------------------------------------------------------------------------------------------- 13 Ni 1 -1.481735453537661e+00 -1.481735453567179e+00 2.95179e-11 3.19110e-10 2 -2.287737916674467e+00 -2.287737916703074e+00 2.86065e-11 6.30677e-10 3 -4.606220452438235e+00 -4.606220452456198e+00 1.79634e-11 1.32520e-10 ----------------------------------------------------------------------------------------------------- 14 Ni 1 4.462911675187389e-01 4.462911675187508e-01 1.19349e-14 3.15606e-11 2 1.060526567659265e+00 1.060526567666686e+00 7.42095e-12 1.58191e-10 3 -5.363226492725969e-01 -5.363226492722009e-01 3.96017e-13 1.00670e-10 ----------------------------------------------------------------------------------------------------- 15 Ni 1 4.025991634624911e+00 4.025991634668741e+00 4.38298e-11 5.25375e-11 2 -1.206890421041652e+00 -1.206890421008887e+00 3.27651e-11 5.68987e-11 3 1.621865272717136e+00 1.621865272729921e+00 1.27858e-11 2.22024e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 1.229748970522312e+00 1.229748970509086e+00 1.32263e-11 2.00526e-10 2 2.929819808796820e+00 2.929819808794342e+00 2.47846e-12 7.56892e-11 3 1.603833485104995e+00 1.603833485047408e+00 5.75877e-11 6.68481e-11 ----------------------------------------------------------------------------------------------------- 17 Ni 1 -2.005082658291240e+00 -2.005082658262165e+00 2.90745e-11 1.42313e-09 * 2 2.942704911818075e-01 2.942704911504572e-01 3.13504e-11 5.41884e-11 3 4.864355075333596e-01 4.864355075087905e-01 2.45691e-11 3.18562e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 4.312531006715554e-01 4.312531006483022e-01 2.32532e-11 2.15957e-10 2 2.087873043295422e+00 2.087873043279045e+00 1.63767e-11 4.81577e-10 3 -1.521143619326996e+00 -1.521143619298276e+00 2.87197e-11 1.05182e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 1.285319567211197e+00 1.285319567198915e+00 1.22822e-11 3.18903e-10 2 -9.243371280151811e-01 -9.243371278840752e-01 1.31106e-10 1.71880e-10 3 1.562790863145508e+00 1.562790863135806e+00 9.70179e-12 7.15763e-10 ----------------------------------------------------------------------------------------------------- 20 Ni 1 3.975745900067116e-01 3.975745900355762e-01 2.88646e-11 1.04287e-10 2 5.299522744400711e-01 5.299522744230976e-01 1.69735e-11 8.56573e-09 * 3 -5.194808166089290e-01 -5.194808165924809e-01 1.64481e-11 1.76701e-09 * ----------------------------------------------------------------------------------------------------- 21 Ni 1 -1.719396003459187e+00 -1.719396003465756e+00 6.56875e-12 1.00627e-10 2 1.713373022226554e-01 1.713373022049008e-01 1.77546e-11 1.17423e-11 3 9.967398956633386e-01 9.967398957931025e-01 1.29764e-10 5.52682e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 4.955341784045757e-01 4.955341784113285e-01 6.75277e-12 2.26356e-10 2 3.383813628151055e+00 3.383813628129475e+00 2.15801e-11 3.21803e-10 3 3.761981968305499e+00 3.761981968313648e+00 8.14948e-12 1.40649e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 4.209963617437315e-01 4.209963617352639e-01 8.46756e-12 5.89793e-11 2 -2.434749610298718e-02 -2.434749612442430e-02 2.14371e-11 9.20700e-11 3 -2.713167037920020e-01 -2.713167037760489e-01 1.59531e-11 8.37957e-12 ----------------------------------------------------------------------------------------------------- 24 Ni 1 -5.070210450275070e-01 -5.070210449898843e-01 3.76227e-11 3.64909e-10 2 7.648439071139544e-01 7.648439071007439e-01 1.32105e-11 2.68671e-10 3 -8.475863684302858e-01 -8.475863684527392e-01 2.24534e-11 9.76262e-11 ----------------------------------------------------------------------------------------------------- 25 Ni 1 -2.806204531903431e-01 -2.806204531908930e-01 5.49893e-13 1.79346e-10 2 -1.342668715551101e+00 -1.342668715533338e+00 1.77629e-11 2.48742e-09 * 3 4.056687190583685e-01 4.056687190515651e-01 6.80345e-12 8.62691e-10 ----------------------------------------------------------------------------------------------------- 26 Ni 1 -1.214591399495819e+00 -1.214591399492659e+00 3.15925e-12 3.20485e-10 2 8.541988004921499e-01 8.541988004813624e-01 1.07875e-11 1.28906e-10 3 -1.174970221649705e+00 -1.174970221642354e+00 7.35056e-12 7.55556e-11 ----------------------------------------------------------------------------------------------------- 27 Ni 1 1.860568657382499e+00 1.860568657385222e+00 2.72316e-12 2.93450e-10 2 -4.334559874436911e+00 -4.334559874380048e+00 5.68630e-11 4.35795e-10 3 2.346558344409869e-01 2.346558344728992e-01 3.19123e-11 2.97644e-09 * ----------------------------------------------------------------------------------------------------- 28 Ni 1 -2.518524689744116e+00 -2.518524689752534e+00 8.41860e-12 1.10081e-10 2 2.416609153541848e+00 2.416609153513971e+00 2.78768e-11 1.85653e-10 3 -2.169864387214113e-01 -2.169864387265467e-01 5.13548e-12 2.13571e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 -1.122034824614194e+00 -1.122034824577091e+00 3.71025e-11 1.19427e-10 2 -1.191048516816883e+00 -1.191048516845318e+00 2.84350e-11 3.59588e-10 3 1.465423410085013e+00 1.465423410103087e+00 1.80735e-11 3.81398e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 5.421958819325107e-02 5.421958811968030e-02 7.35708e-11 1.07146e-10 2 8.563477369802891e-01 8.563477369649953e-01 1.52938e-11 2.10769e-10 3 9.215909725871361e-01 9.215909726166464e-01 2.95103e-11 9.79095e-11 ----------------------------------------------------------------------------------------------------- 31 Ni 1 9.723812501049820e-01 9.723812501137081e-01 8.72613e-12 7.40135e-11 2 -1.078205189946503e+00 -1.078205189936971e+00 9.53237e-12 1.62609e-10 3 5.060649452505290e-01 5.060649452440378e-01 6.49125e-12 2.62866e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.236009551477995e+00 1.236009551453218e+00 2.47773e-11 2.47545e-10 2 9.074982516346604e-01 9.074982516368448e-01 2.18447e-12 6.93479e-11 3 4.714617163154109e-01 4.714617162555243e-01 5.98866e-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 6.527398374298149e-01 3.14471e-12 2.72414e-11 2 5.430295790685866e-01 5.430295790617027e-01 6.88394e-12 5.23304e-11 3 8.547187299026275e-01 8.547187299053128e-01 2.68530e-12 3.50243e-11 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -9.667295427694244e-01 -9.667295427266968e-01 4.27276e-11 9.92509e-11 2 9.474784189903837e-01 9.474784190670293e-01 7.66457e-11 9.14934e-11 3 -1.132668041166899e+00 -1.132668041172438e+00 5.53935e-12 2.45191e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -1.699252573949039e+00 -1.699252573979686e+00 3.06473e-11 4.32006e-10 2 -9.221842678210885e-01 -9.221842678468555e-01 2.57669e-11 7.14786e-09 * 3 -2.192540116790222e-01 -2.192540117183493e-01 3.93271e-11 4.79871e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 5.843655336997411e-01 5.843655336934389e-01 6.30218e-12 7.73079e-11 2 5.965004490197717e-02 5.965004490825696e-02 6.27979e-12 9.39366e-10 3 7.232173927566610e-01 7.232173927040492e-01 5.26118e-11 1.89635e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -2.366083285254588e-01 -2.366083285201244e-01 5.33437e-12 7.47595e-11 2 -7.252367965628517e-02 -7.252367964370890e-02 1.25763e-11 7.83680e-11 3 1.248396187186931e-01 1.248396186870345e-01 3.16586e-11 1.40167e-09 ----------------------------------------------------------------------------------------------------- 6 Ti 1 9.704357729830727e-02 9.704357729855652e-02 2.49245e-13 5.13298e-10 2 -4.196053959729911e-02 -4.196053960186923e-02 4.57012e-12 5.12836e-11 3 1.016373165440305e-01 1.016373165448848e-01 8.54317e-13 2.15257e-09 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -6.247844233402735e-01 -6.247844233457870e-01 5.51348e-12 1.78404e-10 2 -3.849580579459176e-02 -3.849580579443186e-02 1.59900e-13 1.48772e-09 3 1.855982696651431e-01 1.855982696691664e-01 4.02334e-12 1.64034e-09 ----------------------------------------------------------------------------------------------------- 8 Ti 1 1.508297002120724e+00 1.508297002065289e+00 5.54348e-11 4.59637e-10 2 1.917833650167307e+00 1.917833650169706e+00 2.39897e-12 1.75714e-10 3 1.463684934399078e+00 1.463684934372420e+00 2.66582e-11 8.71367e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -2.961403025593950e-01 -2.961403025519708e-01 7.42423e-12 8.84428e-11 2 -7.429802193324659e-01 -7.429802193274303e-01 5.03564e-12 3.25944e-11 3 -1.348538876063481e+00 -1.348538876088960e+00 2.54785e-11 1.48261e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -4.277244242056947e-01 -4.277244241836732e-01 2.20214e-11 7.73154e-11 2 1.757023518399450e+00 1.757023518398748e+00 7.01439e-13 8.40039e-11 3 -1.037652859295609e+00 -1.037652859306039e+00 1.04305e-11 5.61768e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 1.614265627776611e+00 1.614265627825663e+00 4.90514e-11 1.15751e-10 2 -2.032957241278362e+00 -2.032957241286292e+00 7.92966e-12 1.93743e-10 3 2.979806689903293e+00 2.979806689902954e+00 3.38840e-13 2.22466e-09 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -5.037941391232593e-01 -5.037941391272811e-01 4.02178e-12 1.00850e-10 2 1.115722598743622e+00 1.115722598734117e+00 9.50484e-12 1.59483e-10 3 1.560044582887414e+00 1.560044582900445e+00 1.30307e-11 1.61422e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.265458530471868e+00 1.265458530492104e+00 2.02354e-11 9.10185e-11 2 -5.720016329006876e-01 -5.720016328972799e-01 3.40772e-12 5.44340e-10 3 -1.448441072373224e-01 -1.448441072079587e-01 2.93637e-11 1.04425e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -7.029535435623325e-01 -7.029535435769512e-01 1.46186e-11 8.15620e-11 2 -4.812868368261607e-01 -4.812868368736723e-01 4.75116e-11 1.94383e-10 3 1.840584193764408e-01 1.840584193898456e-01 1.34048e-11 9.82422e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 -5.485145419679035e-01 -5.485145419428434e-01 2.50601e-11 8.57986e-11 2 -1.302276164593061e+00 -1.302276164516850e+00 7.62108e-11 2.06654e-09 3 4.342291131943192e-01 4.342291131699206e-01 2.43986e-11 6.40690e-11 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.077237848410424e+00 -1.077237848428896e+00 1.84717e-11 1.42102e-09 2 -2.055287464398690e-01 -2.055287464384384e-01 1.43061e-12 5.23691e-09 * 3 -1.229735149571128e-01 -1.229735149557736e-01 1.33918e-12 1.10947e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 7.719996907137855e-03 7.719996866568516e-03 4.05693e-11 5.66082e-11 2 -6.628372974903890e-01 -6.628372974869241e-01 3.46490e-12 4.07672e-10 3 -5.043025073796854e-01 -5.043025073752490e-01 4.43645e-12 9.49437e-11 ----------------------------------------------------------------------------------------------------- 18 Ti 1 1.525284588609273e+00 1.525284588645806e+00 3.65332e-11 3.41017e-10 2 3.320691333022126e-01 3.320691332684356e-01 3.37770e-11 1.50059e-09 3 -1.816146469343234e+00 -1.816146469346882e+00 3.64730e-12 1.96427e-09 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -5.655759037979985e-01 -5.655759038314709e-01 3.34724e-11 1.85438e-10 2 4.576860081335662e-01 4.576860081487958e-01 1.52296e-11 2.50178e-09 3 7.745805691234264e-01 7.745805691266474e-01 3.22098e-12 1.31498e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 -1.029317862083413e+00 -1.029317862093136e+00 9.72356e-12 1.94843e-10 2 -5.947067811215656e-01 -5.947067811615947e-01 4.00291e-11 6.85459e-11 3 8.740866231524324e-01 8.740866231432044e-01 9.22795e-12 1.03229e-10 ----------------------------------------------------------------------------------------------------- 21 Ti 1 5.973662500971948e-01 5.973662500536866e-01 4.35082e-11 2.36390e-10 2 -9.410559884213346e-01 -9.410559883767160e-01 4.46186e-11 9.62648e-11 3 3.320485930622986e-01 3.320485930307267e-01 3.15719e-11 1.21749e-09 ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.309070818894081e+00 1.309070818992311e+00 9.82296e-11 1.26823e-09 2 2.028265642595165e+00 2.028265642602241e+00 7.07567e-12 2.55441e-10 3 4.898376762406870e-01 4.898376762542467e-01 1.35597e-11 3.08848e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -9.287403414580504e-01 -9.287403414430022e-01 1.50482e-11 9.26326e-10 2 8.376390960929549e-01 8.376390960936202e-01 6.65246e-13 1.57433e-10 3 -8.660090183051998e-01 -8.660090183043623e-01 8.37552e-13 1.89590e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -1.289875017369488e+00 -1.289875017305119e+00 6.43694e-11 1.10767e-10 2 -1.386994062574681e+00 -1.386994062579655e+00 4.97358e-12 4.98304e-09 * 3 -7.088372519529168e-01 -7.088372519796993e-01 2.67825e-11 4.07579e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -1.049960263444435e+00 -1.049960263450994e+00 6.55875e-12 1.63699e-09 2 -1.304973199505282e+00 -1.304973199514319e+00 9.03655e-12 1.98191e-10 3 -3.469859529855925e+00 -3.469859529840246e+00 1.56786e-11 1.77505e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 1.189837543626615e+00 1.189837543604775e+00 2.18396e-11 2.47221e-10 2 2.425190897363744e-02 2.425190901777783e-02 4.41404e-11 1.87992e-10 3 -3.510579792690104e+00 -3.510579792684124e+00 5.97966e-12 9.32454e-11 ----------------------------------------------------------------------------------------------------- 27 Ti 1 3.996786837510817e+00 3.996786837536855e+00 2.60378e-11 1.12889e-10 2 -5.034170823591134e-01 -5.034170823568680e-01 2.24543e-12 8.58319e-10 3 1.394045567823264e+00 1.394045567837358e+00 1.40938e-11 4.85532e-11 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -1.931885997848007e+00 -1.931885997817612e+00 3.03946e-11 3.17451e-11 2 1.939734658437256e+00 1.939734658410982e+00 2.62739e-11 1.80819e-10 3 2.055567923385087e+00 2.055567923391859e+00 6.77192e-12 1.18888e-10 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -9.734500295149924e-01 -9.734500295276671e-01 1.26748e-11 1.43598e-09 2 6.245220731644181e-01 6.245220731736287e-01 9.21063e-12 2.66830e-10 3 4.692800393453733e-01 4.692800393274036e-01 1.79697e-11 1.65698e-09 ----------------------------------------------------------------------------------------------------- 30 Ti 1 4.474406939686663e-01 4.474406939927376e-01 2.40712e-11 2.43422e-10 2 6.055440779668081e-01 6.055440779771941e-01 1.03860e-11 3.78142e-10 3 -1.250080190848967e+00 -1.250080190843192e+00 5.77516e-12 1.66905e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 5.082449121328265e-01 5.082449121431151e-01 1.02885e-11 1.57971e-09 2 -7.868870980007979e-01 -7.868870979793861e-01 2.14119e-11 1.92746e-10 3 4.632707891159231e-01 4.632707891178928e-01 1.96976e-12 8.97066e-11 ----------------------------------------------------------------------------------------------------- 32 Ti 1 -4.513766666109433e-01 -4.513766666099078e-01 1.03556e-12 4.35565e-11 2 -5.973837652243081e-01 -5.973837652096916e-01 1.46165e-11 9.52648e-11 3 6.671933221792831e-01 6.671933221530448e-01 2.62382e-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 = ----------------------- = 5.25510e-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 8.838151525827082e-01 9.37472e-13 4.06452e-10 2 5.893687025942497e-01 5.893687025963914e-01 2.14173e-12 2.52611e-11 3 -1.520046180531092e-01 -1.520046180595526e-01 6.44343e-12 5.71723e-10 ----------------------------------------------------------------------------------------------------- 2 Ni 1 -1.263405625671584e+00 -1.263405625539550e+00 1.32034e-10 2.67987e-10 2 -1.274639802414578e+00 -1.274639802411802e+00 2.77689e-12 3.58723e-10 3 1.160199545906072e+00 1.160199545923947e+00 1.78755e-11 7.02456e-10 ----------------------------------------------------------------------------------------------------- 3 Ni 1 6.634719462920441e-01 6.634719462928687e-01 8.24563e-13 7.77899e-11 2 -3.144045840328843e-01 -3.144045840322164e-01 6.67910e-13 2.58409e-10 3 -3.366731552333211e-01 -3.366731552229798e-01 1.03413e-11 1.63402e-10 ----------------------------------------------------------------------------------------------------- 4 Ti 1 1.118727329272745e+00 1.118727329254486e+00 1.82585e-11 3.99289e-11 2 -3.935052633608275e+00 -3.935052633620705e+00 1.24296e-11 1.07896e-10 3 -1.100326248707049e+00 -1.100326248699894e+00 7.15561e-12 1.42759e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -1.326363624040317e+00 -1.326363624075002e+00 3.46856e-11 1.68779e-10 2 4.322299584288852e-01 4.322299584518846e-01 2.29993e-11 5.06946e-11 3 -1.421313819594814e-01 -1.421313819454233e-01 1.40581e-11 4.20718e-11 ----------------------------------------------------------------------------------------------------- 6 Ni 1 1.553373594970380e+00 1.553373594970267e+00 1.13243e-13 2.17595e-11 2 1.847567560093200e+00 1.847567560095634e+00 2.43472e-12 1.00697e-10 3 -1.738609390639726e+00 -1.738609390645958e+00 6.23235e-12 2.33523e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 -3.440334259884424e+00 -3.440334259899212e+00 1.47882e-11 1.25152e-09 2 -4.388583521393639e+00 -4.388583521423924e+00 3.02851e-11 1.47137e-10 3 1.623863346338508e+00 1.623863346328008e+00 1.05000e-11 3.51588e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -6.991097407508263e+00 -6.991097407488907e+00 1.93570e-11 6.48950e-09 * 2 -3.651906909009946e+00 -3.651906908988275e+00 2.16707e-11 3.45253e-10 3 2.937994940901720e+00 2.937994940961315e+00 5.95950e-11 1.49286e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 3.806790171790535e+00 3.806790171786709e+00 3.82672e-12 1.23318e-10 2 -2.059924279211204e+00 -2.059924279230409e+00 1.92051e-11 2.43708e-10 3 -1.192112728720338e+00 -1.192112728728940e+00 8.60179e-12 1.15989e-11 ----------------------------------------------------------------------------------------------------- 10 Ni 1 -2.526968711356154e+00 -2.526968711370021e+00 1.38676e-11 5.05329e-10 2 -6.183913077295627e-02 -6.183913077702254e-02 4.06627e-12 1.09042e-10 3 -1.530971777723654e+00 -1.530971777748687e+00 2.50331e-11 3.69852e-10 ----------------------------------------------------------------------------------------------------- 11 Ni 1 6.824239089486267e-02 6.824239092974076e-02 3.48781e-11 5.48406e-10 2 -2.708165464366652e+00 -2.708165464355933e+00 1.07190e-11 1.08094e-08 * 3 -2.814613022352395e+00 -2.814613022332925e+00 1.94698e-11 1.41072e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 -1.837678090056894e+00 -1.837678090056054e+00 8.39551e-13 9.82534e-10 2 6.717145325511911e+00 6.717145325475662e+00 3.62492e-11 3.67318e-10 3 2.215376018012892e+00 2.215376018083043e+00 7.01510e-11 7.03828e-11 ----------------------------------------------------------------------------------------------------- 13 Ti 1 -1.389798833261096e-01 -1.389798833126172e-01 1.34924e-11 3.74007e-10 2 7.759356983018590e-01 7.759356982635194e-01 3.83397e-11 3.29976e-10 3 -8.470515963504907e-01 -8.470515962677799e-01 8.27107e-11 2.32665e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -2.313559316488059e-01 -2.313559316830869e-01 3.42810e-11 9.48198e-11 2 -2.477908499708986e+00 -2.477908499705801e+00 3.18456e-12 2.02713e-11 3 -1.912763783213503e+00 -1.912763783203943e+00 9.55946e-12 1.15553e-09 ----------------------------------------------------------------------------------------------------- 15 Ni 1 1.093036558418017e+00 1.093036558430275e+00 1.22586e-11 1.64966e-10 2 1.248875382654191e+00 1.248875382646268e+00 7.92300e-12 4.62352e-10 3 1.800995641808863e+00 1.800995641745099e+00 6.37639e-11 5.17781e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 3.094424578324388e+00 3.094424578214078e+00 1.10309e-10 2.49274e-10 2 -2.629931402306858e-01 -2.629931402342820e-01 3.59623e-12 4.90050e-11 3 3.574947375380994e+00 3.574947375524329e+00 1.43335e-10 9.46984e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 1.220485450360840e+00 1.220485450365029e+00 4.18909e-12 9.22877e-11 2 9.936349208353320e-01 9.936349208169022e-01 1.84298e-11 8.54856e-11 3 1.715821730168317e-01 1.715821730172714e-01 4.39732e-13 1.00482e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 -3.513846843196242e-01 -3.513846843408008e-01 2.11766e-11 5.18200e-11 2 7.934708327582733e-01 7.934708328202021e-01 6.19288e-11 8.24014e-11 3 -2.146668179693053e-02 -2.146668180946577e-02 1.25352e-11 2.33335e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 -6.177599200170270e-02 -6.177599199963958e-02 2.06311e-12 4.04674e-11 2 1.093618997918711e+00 1.093618997884835e+00 3.38756e-11 1.18753e-10 3 -8.818855711473637e-01 -8.818855711372701e-01 1.00936e-11 4.37501e-11 ----------------------------------------------------------------------------------------------------- 20 Ni 1 -3.967597335173161e-01 -3.967597335241072e-01 6.79107e-12 1.10350e-10 2 -7.526334636205608e-01 -7.526334636549389e-01 3.43781e-11 3.75022e-11 3 -7.193571278397785e-01 -7.193571278371516e-01 2.62690e-12 3.92527e-10 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -2.208908645421457e+00 -2.208908645438165e+00 1.67080e-11 1.40872e-10 2 -1.657563908166854e+00 -1.657563908182030e+00 1.51767e-11 1.21625e-08 * 3 -9.915472413886279e+00 -9.915472413767931e+00 1.18348e-10 1.04396e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 8.271789684676918e+00 8.271789684647946e+00 2.89724e-11 2.01971e-08 * 2 9.534187419478517e+00 9.534187419432929e+00 4.55884e-11 3.72120e-10 3 8.143456529842233e+00 8.143456530001195e+00 1.58963e-10 3.74245e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 5.341980592113020e-01 5.341980592123341e-01 1.03206e-12 8.21965e-11 2 3.891687741078582e-01 3.891687740673530e-01 4.05052e-11 3.94730e-10 3 -3.590120422635090e-01 -3.590120423135896e-01 5.00806e-11 2.16541e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -4.060551397272155e-01 -4.060551397469042e-01 1.96886e-11 6.94209e-10 2 -1.594396929447933e+00 -1.594396929427204e+00 2.07290e-11 1.18320e-10 3 -5.344376140417908e-01 -5.344376140781000e-01 3.63092e-11 1.00839e-09 ----------------------------------------------------------------------------------------------------- 25 Ti 1 -8.341386173457146e-01 -8.341386172554843e-01 9.02303e-11 7.80441e-11 2 4.886751335750932e-01 4.886751335777066e-01 2.61335e-12 2.50754e-10 3 4.054705799666269e+00 4.054705799661157e+00 5.11235e-12 3.57299e-09 * ----------------------------------------------------------------------------------------------------- 26 Ti 1 7.391679264576060e-01 7.391679264576565e-01 5.05151e-14 2.18702e-09 * 2 1.834254447056690e+00 1.834254447021231e+00 3.54592e-11 1.07569e-10 3 -3.013259254604746e+00 -3.013259254559141e+00 4.56049e-11 1.12849e-09 ----------------------------------------------------------------------------------------------------- 27 Ti 1 3.040360911008413e+00 3.040360910981289e+00 2.71236e-11 7.44616e-10 2 -2.826618859583812e+00 -2.826618859591369e+00 7.55707e-12 1.14152e-10 3 1.199460250973278e+00 1.199460250964374e+00 8.90354e-12 3.30079e-09 * ----------------------------------------------------------------------------------------------------- 28 Ti 1 -2.241278693402642e+00 -2.241278693409276e+00 6.63336e-12 1.11490e-10 2 1.147159275215330e+00 1.147159275216561e+00 1.23102e-12 6.40445e-11 3 8.731527937591850e-01 8.731527937847516e-01 2.55667e-11 9.20700e-10 ----------------------------------------------------------------------------------------------------- 29 Ni 1 -8.081603768562442e+00 -8.081603768594128e+00 3.16867e-11 4.52028e-10 2 -3.102171386515059e+00 -3.102171386398984e+00 1.16075e-10 5.46057e-10 3 -3.399831194442594e+00 -3.399831194478654e+00 3.60596e-11 6.10969e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 2.721766177929751e+00 2.721766177852757e+00 7.69935e-11 6.36842e-10 2 -1.799090787834973e+00 -1.799090787841022e+00 6.04872e-12 6.16004e-10 3 5.843512898270020e+00 5.843512898270210e+00 1.90070e-13 2.74622e-09 * ----------------------------------------------------------------------------------------------------- 31 Ti 1 3.400321118795637e+00 3.400321118835422e+00 3.97851e-11 9.14455e-11 2 5.821702724694950e+00 5.821702724724284e+00 2.93348e-11 3.41513e-11 3 -2.334701082651225e+00 -2.334701082669560e+00 1.83356e-11 1.52243e-09 ----------------------------------------------------------------------------------------------------- 32 Ni 1 1.281177568054588e-01 1.281177567928119e-01 1.26469e-11 1.21412e-10 2 -8.391018533060480e-01 -8.391018532984653e-01 7.58271e-12 2.36280e-09 * 3 -6.525666282495745e-01 -6.525666282756095e-01 2.60351e-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 = ----------------------- = 5.83939e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 5.25510e-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 5.25510e-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.