!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_LeeShim_2004_NiCu__MO_409065472403_000 Supported species : Cu Ni 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 = Cu | a0 = 3.6133155822753906 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 2.745433797343044e-01 2.745433797468635e-01 1.25591e-11 3.11168e-11 2 -5.595297820560207e-01 -5.595297820549118e-01 1.10889e-12 1.34317e-10 3 -8.170859627321043e-01 -8.170859627699547e-01 3.78504e-11 9.10602e-11 ----------------------------------------------------------------------------------------------------- 2 Cu 1 -2.230222630192352e+00 -2.230222630178170e+00 1.41820e-11 7.32419e-11 2 2.177954294281902e+00 2.177954294284056e+00 2.15383e-12 2.06186e-11 3 5.775715298678857e-01 5.775715298650502e-01 2.83551e-12 4.17479e-10 ----------------------------------------------------------------------------------------------------- 3 Cu 1 1.194280974277197e+00 1.194280974279986e+00 2.78910e-12 1.85771e-11 2 3.786803570133325e-01 3.786803570167923e-01 3.45979e-12 1.31342e-10 3 -4.266925646736679e-01 -4.266925646788534e-01 5.18552e-12 3.85739e-10 ----------------------------------------------------------------------------------------------------- 4 Cu 1 6.700123419700094e-01 6.700123419644817e-01 5.52769e-12 1.99444e-09 * 2 1.044210745105748e+00 1.044210745130227e+00 2.44793e-11 2.12188e-11 3 9.550672962261660e-01 9.550672962238927e-01 2.27329e-12 6.32411e-11 ----------------------------------------------------------------------------------------------------- 5 Cu 1 1.031674601628760e+00 1.031674601626257e+00 2.50289e-12 6.25693e-11 2 -2.212814528525098e+00 -2.212814528518988e+00 6.10978e-12 7.05467e-11 3 5.120031497029663e-01 5.120031497071327e-01 4.16633e-12 9.77958e-11 ----------------------------------------------------------------------------------------------------- 6 Cu 1 1.184312117197179e-01 1.184312117289711e-01 9.25317e-12 6.02968e-11 2 1.095462401432048e+00 1.095462401438727e+00 6.67844e-12 5.17195e-11 3 1.880277507004906e-01 1.880277506992431e-01 1.24750e-12 3.92776e-10 ----------------------------------------------------------------------------------------------------- 7 Cu 1 1.151446221271679e+00 1.151446221256867e+00 1.48128e-11 7.77525e-11 2 -3.122530986970882e+00 -3.122530986937681e+00 3.32010e-11 3.33382e-11 3 -3.229736313293790e+00 -3.229736313350663e+00 5.68732e-11 2.59216e-10 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -2.152251624818760e+00 -2.152251624841475e+00 2.27156e-11 1.57181e-11 2 -7.771366105638252e-01 -7.771366105739764e-01 1.01512e-11 2.02478e-10 3 -7.346893576396191e-01 -7.346893576695878e-01 2.99687e-11 3.74003e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 -1.278451557975945e-02 -1.278451557020344e-02 9.55601e-12 6.39397e-10 2 -1.202047279508019e+00 -1.202047279481541e+00 2.64775e-11 2.74594e-10 3 -3.636053287291564e-01 -3.636053287283522e-01 8.04246e-13 8.73113e-11 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -1.265061798308087e+00 -1.265061798297274e+00 1.08125e-11 5.57934e-10 2 1.373322470566937e+00 1.373322470507807e+00 5.91303e-11 1.99884e-10 3 -1.513021876775570e+00 -1.513021876781852e+00 6.28142e-12 2.43336e-11 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -3.660992388296481e-01 -3.660992388440301e-01 1.43820e-11 1.27458e-10 2 -1.526232123815146e+00 -1.526232123820519e+00 5.37304e-12 1.83977e-10 3 3.822281410616429e-01 3.822281410847214e-01 2.30785e-11 1.05010e-08 * ----------------------------------------------------------------------------------------------------- 12 Cu 1 3.245283531440227e-01 3.245283531671557e-01 2.31329e-11 6.40551e-09 * 2 7.671033472120464e-01 7.671033472118270e-01 2.19380e-13 3.69631e-11 3 6.709628189395491e-01 6.709628189491120e-01 9.56291e-12 8.67278e-11 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -1.171373908268712e+00 -1.171373908251197e+00 1.75149e-11 2.31684e-10 2 -2.577520287513674e+00 -2.577520287576426e+00 6.27525e-11 1.36100e-10 3 -3.321806603791901e+00 -3.321806603823696e+00 3.17955e-11 1.95467e-10 ----------------------------------------------------------------------------------------------------- 14 Cu 1 2.439247958804759e-01 2.439247958968027e-01 1.63268e-11 1.30202e-09 * 2 9.730163348795610e-01 9.730163348987768e-01 1.92159e-11 8.72002e-11 3 -1.608123414120059e-01 -1.608123414106107e-01 1.39519e-12 4.80376e-11 ----------------------------------------------------------------------------------------------------- 15 Cu 1 2.981312878023780e+00 2.981312877929081e+00 9.46998e-11 3.12425e-10 2 -1.424094790869627e+00 -1.424094790828435e+00 4.11922e-11 4.85529e-10 3 1.239371827758944e+00 1.239371827772491e+00 1.35476e-11 1.05292e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 1.345763363839813e+00 1.345763363833396e+00 6.41731e-12 9.70886e-11 2 2.082462513090631e+00 2.082462513116120e+00 2.54894e-11 8.69140e-11 3 1.631425074542906e+00 1.631425074575506e+00 3.26004e-11 8.82697e-10 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -6.766585369633743e-01 -6.766585369516287e-01 1.17456e-11 1.95718e-11 2 -6.174129784764505e-01 -6.174129784919213e-01 1.54708e-11 1.69602e-11 3 -4.965883521309116e-01 -4.965883521723970e-01 4.14854e-11 1.16489e-10 ----------------------------------------------------------------------------------------------------- 18 Cu 1 6.775174665071497e-01 6.775174665531871e-01 4.60374e-11 1.25208e-10 2 1.068562651160894e+00 1.068562651169318e+00 8.42348e-12 1.37701e-10 3 -2.710241029755106e-01 -2.710241029311747e-01 4.43359e-11 3.70360e-10 ----------------------------------------------------------------------------------------------------- 19 Cu 1 5.306008134894602e-01 5.306008134724206e-01 1.70396e-11 5.16214e-09 * 2 2.035763794244479e-01 2.035763793403582e-01 8.40897e-11 7.63465e-10 3 -2.419492974370146e-01 -2.419492974127354e-01 2.42792e-11 1.09962e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 1.573111382677126e-01 1.573111382571774e-01 1.05352e-11 3.20547e-10 2 1.159066857087585e+00 1.159066857074102e+00 1.34832e-11 1.93142e-10 3 2.442513741706142e-01 2.442513741430863e-01 2.75278e-11 9.49946e-12 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.981172041444147e+00 -1.981172041346083e+00 9.80642e-11 2.81496e-10 2 -1.312653838249158e-01 -1.312653838181128e-01 6.80297e-12 3.27684e-10 3 1.717357570026212e+00 1.717357569904833e+00 1.21379e-10 2.38843e-10 ----------------------------------------------------------------------------------------------------- 22 Cu 1 1.133122548824512e+00 1.133122548859384e+00 3.48721e-11 1.74524e-10 2 3.124655603417887e+00 3.124655603413931e+00 3.95639e-12 9.50919e-11 3 2.741324787512866e+00 2.741324787512791e+00 7.50511e-14 1.50695e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -6.649646418154531e-01 -6.649646418597474e-01 4.42942e-11 4.09048e-10 2 4.975395933194559e-01 4.975395933312369e-01 1.17810e-11 4.41902e-11 3 -5.934434449837348e-01 -5.934434450364331e-01 5.26983e-11 1.53702e-10 ----------------------------------------------------------------------------------------------------- 24 Cu 1 4.480218384884510e-01 4.480218384109307e-01 7.75203e-11 2.31772e-10 2 -2.153418225771029e-01 -2.153418226087386e-01 3.16356e-11 1.58454e-10 3 -7.389792420287212e-01 -7.389792421224786e-01 9.37573e-11 3.78778e-10 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -1.820532478732534e+00 -1.820532478698097e+00 3.44367e-11 5.09048e-10 2 -1.111381117607894e+00 -1.111381117559765e+00 4.81293e-11 1.68478e-10 3 2.132989033807757e-01 2.132989033330184e-01 4.77573e-11 1.41129e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -1.034976138385057e+00 -1.034976138426721e+00 4.16638e-11 3.11191e-10 2 1.595437433457798e+00 1.595437433436132e+00 2.16667e-11 4.95128e-10 3 -2.037243582692258e+00 -2.037243582709261e+00 1.70037e-11 2.77276e-08 * ----------------------------------------------------------------------------------------------------- 27 Cu 1 2.081308978222526e+00 2.081308978247169e+00 2.46425e-11 1.10993e-10 2 -3.762635274925514e+00 -3.762635274897974e+00 2.75397e-11 1.17635e-10 3 1.498109120254139e+00 1.498109120214771e+00 3.93678e-11 8.64904e-11 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -1.666025805229884e+00 -1.666025805218800e+00 1.10845e-11 1.89581e-09 * 2 1.770745370627270e+00 1.770745370643365e+00 1.60953e-11 2.10888e-10 3 -3.258037772921600e-01 -3.258037772677957e-01 2.43643e-11 2.72944e-10 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -1.050777094497039e+00 -1.050777094408060e+00 8.89786e-11 5.35602e-10 2 -9.031986992509551e-01 -9.031986991925668e-01 5.83883e-11 7.62164e-11 3 1.872393072924642e-01 1.872393072912901e-01 1.17414e-12 4.02193e-10 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -2.931839011344896e-01 -2.931839011213373e-01 1.31523e-11 3.85031e-11 2 8.245221845390371e-01 8.245221845352649e-01 3.77220e-12 1.37874e-10 3 5.521839021173441e-01 5.521839021048186e-01 1.25255e-11 1.42497e-10 ----------------------------------------------------------------------------------------------------- 31 Cu 1 7.780474150127139e-01 7.780474150287929e-01 1.60790e-11 2.69775e-10 2 -9.806248743089876e-01 -9.806248743059708e-01 3.01681e-12 3.15052e-10 3 7.261834107178274e-01 7.261834107111385e-01 6.68898e-12 1.00159e-09 ----------------------------------------------------------------------------------------------------- 32 Cu 1 1.244236033897009e+00 1.244236033926878e+00 2.98690e-11 1.12016e-09 2 9.874480041775273e-01 9.874480041702638e-01 7.26352e-12 5.15456e-09 * 3 1.235876184315331e+00 1.235876184318030e+00 2.69829e-12 1.58786e-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 = 9, direction = 1: |F_model - F_numer| error = ----------------------- = 7.47468e-10 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Ni | a0 = 3.5213918685913086 | (Configuration in file "config-Ni.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ni 1 -1.802305036285645e+00 -1.802305036282770e+00 2.87503e-12 2.98817e-11 2 3.312368745502601e-01 3.312368745186933e-01 3.15669e-11 4.47424e-11 3 -1.713300062980399e+00 -1.713300062978069e+00 2.32969e-12 1.77287e-11 ----------------------------------------------------------------------------------------------------- 2 Ni 1 1.221669649017856e+00 1.221669649007885e+00 9.97069e-12 2.99714e-11 2 2.643913825447134e-01 2.643913825253932e-01 1.93203e-11 1.96750e-10 3 -1.277440391868809e+00 -1.277440391858028e+00 1.07807e-11 3.48639e-10 ----------------------------------------------------------------------------------------------------- 3 Ni 1 2.776800477442771e+00 2.776800477460259e+00 1.74887e-11 1.23954e-09 * 2 -2.355267966798683e+00 -2.355267966857407e+00 5.87246e-11 6.72636e-09 * 3 2.862646012751742e+00 2.862646012726535e+00 2.52065e-11 1.61617e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 -1.127110982988807e+00 -1.127110983001326e+00 1.25189e-11 2.64626e-10 2 9.296425675220168e-01 9.296425675375051e-01 1.54883e-11 5.99095e-11 3 1.830837081340020e+00 1.830837081331404e+00 8.61555e-12 4.12752e-11 ----------------------------------------------------------------------------------------------------- 5 Ni 1 6.443209722887851e-02 6.443209721342082e-02 1.54577e-11 7.96908e-11 2 8.896856264934381e-01 8.896856264924381e-01 9.99978e-13 4.66371e-10 3 6.740487004400751e-01 6.740487004786762e-01 3.86010e-11 4.19298e-10 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -1.757722945480572e-02 -1.757722944306734e-02 1.17384e-11 6.48709e-11 2 4.212344374838504e+00 4.212344374811322e+00 2.71818e-11 3.19318e-10 3 -3.472104396805039e+00 -3.472104396800456e+00 4.58300e-12 2.23358e-10 ----------------------------------------------------------------------------------------------------- 7 Ni 1 9.519685791414539e-01 9.519685790588451e-01 8.26088e-11 1.82671e-10 2 -4.143336873930378e+00 -4.143336874026459e+00 9.60805e-11 1.25895e-10 3 1.844404400434257e+00 1.844404400432765e+00 1.49192e-12 2.66323e-10 ----------------------------------------------------------------------------------------------------- 8 Ni 1 1.110768636683277e+00 1.110768636854882e+00 1.71605e-10 2.02083e-10 2 1.840527168720998e+00 1.840527168502315e+00 2.18683e-10 5.27158e-10 3 -2.008768876104219e+00 -2.008768876162669e+00 5.84492e-11 2.11427e-10 ----------------------------------------------------------------------------------------------------- 9 Ni 1 -1.730731851881617e+00 -1.730731851910717e+00 2.90998e-11 1.79112e-10 2 -7.417631304685285e+00 -7.417631304677277e+00 8.00782e-12 2.86046e-10 3 -5.910497826614387e+00 -5.910497826608110e+00 6.27676e-12 1.45969e-10 ----------------------------------------------------------------------------------------------------- 10 Ni 1 1.613347553613520e+00 1.613347553626802e+00 1.32825e-11 1.61624e-10 2 1.409283125527643e+00 1.409283125513333e+00 1.43103e-11 1.45439e-10 3 -1.212396473022749e+00 -1.212396472989297e+00 3.34524e-11 8.93097e-11 ----------------------------------------------------------------------------------------------------- 11 Ni 1 -4.247851411840748e+00 -4.247851411796746e+00 4.40021e-11 1.00380e-10 2 8.132642938213088e-01 8.132642938791743e-01 5.78655e-11 6.33007e-10 3 -4.956295809136378e+00 -4.956295809116780e+00 1.95985e-11 1.76329e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 -5.176278040244844e-01 -5.176278039986397e-01 2.58447e-11 2.99755e-10 2 6.153497823431398e+00 6.153497823418759e+00 1.26397e-11 1.08978e-10 3 7.587239680637197e+00 7.587239680630829e+00 6.36735e-12 3.30847e-10 ----------------------------------------------------------------------------------------------------- 13 Ni 1 8.287735694065423e-01 8.287735694137732e-01 7.23088e-12 7.96873e-11 2 -8.012942015957959e-01 -8.012942015953083e-01 4.87610e-13 8.40947e-11 3 1.063897326267589e+00 1.063897326260265e+00 7.32392e-12 6.09332e-10 ----------------------------------------------------------------------------------------------------- 14 Ni 1 -1.775499210239696e-01 -1.775499210426720e-01 1.87024e-11 1.19708e-11 2 -5.547766940094179e-01 -5.547766940081404e-01 1.27742e-12 7.09678e-11 3 7.312190969439717e-01 7.312190969891880e-01 4.52163e-11 9.88760e-11 ----------------------------------------------------------------------------------------------------- 15 Ni 1 -8.884298991138759e-01 -8.884298991582115e-01 4.43355e-11 9.25048e-09 * 2 1.341314974845577e+00 1.341314974820047e+00 2.55296e-11 2.46200e-10 3 -1.082467219061209e+00 -1.082467219033552e+00 2.76572e-11 3.32114e-10 ----------------------------------------------------------------------------------------------------- 16 Ni 1 -1.895570544342849e+00 -1.895570544283309e+00 5.95404e-11 3.09712e-10 2 -1.174794624581088e+00 -1.174794624581380e+00 2.92655e-13 2.37287e-10 3 -9.481348779222737e-01 -9.481348778941004e-01 2.81732e-11 2.71693e-10 ----------------------------------------------------------------------------------------------------- 17 Ni 1 -1.593519001707517e+00 -1.593519001711399e+00 3.88156e-12 2.53200e-10 2 9.599896606623175e-01 9.599896606355840e-01 2.67335e-11 1.36184e-10 3 -2.418747956546316e+00 -2.418747956519531e+00 2.67852e-11 3.39568e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 -1.176077623577501e-01 -1.176077625026921e-01 1.44942e-10 3.55713e-08 * 2 -7.113950940642762e+00 -7.113950940584101e+00 5.86606e-11 6.52717e-10 3 -4.078417765424651e+00 -4.078417765428305e+00 3.65397e-12 9.46857e-10 ----------------------------------------------------------------------------------------------------- 19 Ni 1 2.604719849099532e+00 2.604719849087823e+00 1.17084e-11 4.00475e-11 2 2.811945827531478e-01 2.811945827578848e-01 4.73693e-12 5.02083e-10 3 1.754252038458583e+00 1.754252038485832e+00 2.72495e-11 5.27435e-10 ----------------------------------------------------------------------------------------------------- 20 Ni 1 -2.631225624710537e+00 -2.631225624736389e+00 2.58518e-11 3.70771e-10 2 -1.128900217938358e+00 -1.128900218023075e+00 8.47176e-11 2.68864e-10 3 2.383631960216220e+00 2.383631960185531e+00 3.06888e-11 1.21935e-10 ----------------------------------------------------------------------------------------------------- 21 Ni 1 -4.121932136241072e+00 -4.121932136384800e+00 1.43728e-10 2.26846e-10 2 -2.853561467208556e+00 -2.853561467240408e+00 3.18514e-11 2.20616e-10 3 3.205967222243639e+00 3.205967222213798e+00 2.98410e-11 8.99318e-10 ----------------------------------------------------------------------------------------------------- 22 Ni 1 3.155081766275803e+00 3.155081766260878e+00 1.49254e-11 1.28368e-09 * 2 2.093604378359209e+00 2.093604378379704e+00 2.04947e-11 1.66048e-10 3 -2.199121828310978e+00 -2.199121828436583e+00 1.25605e-10 8.58214e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 5.590066771521669e-01 5.590066771490642e-01 3.10274e-12 2.59226e-11 2 -1.700934838819091e+00 -1.700934838805180e+00 1.39111e-11 2.77878e-10 3 1.022878012448255e+00 1.022878012447214e+00 1.04072e-12 1.54647e-10 ----------------------------------------------------------------------------------------------------- 24 Ni 1 -3.564196413510565e+00 -3.564196413502979e+00 7.58549e-12 1.87650e-10 2 2.928340087269821e-02 2.928340091095679e-02 3.82586e-11 1.67217e-10 3 2.597367806183417e+00 2.597367806230517e+00 4.71005e-11 1.22068e-08 * ----------------------------------------------------------------------------------------------------- 25 Ni 1 -2.095825421901150e+00 -2.095825421984236e+00 8.30864e-11 3.74469e-11 2 1.481021241629451e+00 1.481021241609279e+00 2.01728e-11 1.00989e-10 3 -2.607435958384422e+00 -2.607435958394135e+00 9.71312e-12 4.39333e-11 ----------------------------------------------------------------------------------------------------- 26 Ni 1 8.328945151504853e-01 8.328945151687795e-01 1.82943e-11 2.54233e-10 2 6.038894445939248e-02 6.038894442811555e-02 3.12769e-11 2.81018e-10 3 1.356716267239179e+00 1.356716267241122e+00 1.94333e-12 2.43242e-10 ----------------------------------------------------------------------------------------------------- 27 Ni 1 2.079282150138038e+00 2.079282150155509e+00 1.74714e-11 3.72992e-10 2 3.689909890306721e+00 3.689909890227126e+00 7.95950e-11 1.31046e-09 * 3 4.243567980817645e+00 4.243567980641122e+00 1.76524e-10 1.82705e-10 ----------------------------------------------------------------------------------------------------- 28 Ni 1 3.941717446752158e-01 3.941717446731735e-01 2.04231e-12 1.24953e-10 2 -6.205372976565083e-01 -6.205372976177299e-01 3.87784e-11 2.00984e-10 3 -1.018596450885579e+00 -1.018596450904369e+00 1.87907e-11 8.67466e-11 ----------------------------------------------------------------------------------------------------- 29 Ni 1 7.896814512570282e+00 7.896814512593637e+00 2.33547e-11 1.45624e-09 * 2 4.159570344375957e+00 4.159570343896550e+00 4.79407e-10 7.84314e-10 3 2.763550449960014e+00 2.763550449896268e+00 6.37459e-11 6.95755e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 7.469104338337096e-01 7.469104338293664e-01 4.34319e-12 3.04270e-10 2 -1.131021151195636e+00 -1.131021151058824e+00 1.36812e-10 4.74178e-10 3 5.810596354374021e-01 5.810596354706037e-01 3.32016e-11 2.06619e-10 ----------------------------------------------------------------------------------------------------- 31 Ni 1 3.662531906572778e-01 3.662531906468061e-01 1.04717e-11 2.91896e-09 * 2 9.987227491381635e-01 9.987227491264149e-01 1.17486e-11 4.33839e-11 3 -9.714082191574579e-01 -9.714082191504690e-01 6.98885e-12 2.87465e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 -6.738343607014113e-01 -6.738343606851978e-01 1.62136e-11 9.57537e-11 2 -9.428658257913543e-01 -9.428658257927083e-01 1.35403e-12 4.18343e-09 * 3 -6.281495595943402e-01 -6.281495596797682e-01 8.54280e-11 3.58542e-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 = 24, direction = 2: |F_model - F_numer| error = ----------------------- = 1.30649e-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 = Cu Ni | a0 = 3.5665426663130346 | (Configuration in file "config-CuNi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 -5.499051290563726e-01 -5.499051290560215e-01 3.51053e-13 8.36830e-10 2 6.975532118366345e-01 6.975532118351320e-01 1.50258e-12 3.52451e-11 3 -5.501402918927044e-01 -5.501402918844219e-01 8.28249e-12 7.11426e-11 ----------------------------------------------------------------------------------------------------- 2 Ni 1 4.672564634985563e-01 4.672564635024100e-01 3.85370e-12 1.12129e-10 2 -8.341572486379438e-01 -8.341572486221175e-01 1.58263e-11 3.24374e-10 3 7.132868948644923e-01 7.132868948469580e-01 1.75343e-11 5.16152e-11 ----------------------------------------------------------------------------------------------------- 3 Cu 1 6.869237972340064e-01 6.869237972415980e-01 7.59159e-12 2.35871e-10 2 6.011795616619756e-01 6.011795616402147e-01 2.17609e-11 1.60298e-10 3 3.969322227321244e-01 3.969322227170597e-01 1.50647e-11 1.97117e-10 ----------------------------------------------------------------------------------------------------- 4 Ni 1 7.759220696032670e-01 7.759220696257834e-01 2.25163e-11 5.06564e-09 * 2 -1.415717618796646e+00 -1.415717618770790e+00 2.58562e-11 8.81886e-11 3 9.942947206687935e-01 9.942947207032196e-01 3.44260e-11 5.65277e-11 ----------------------------------------------------------------------------------------------------- 5 Ni 1 -4.722759429090682e-01 -4.722759429069781e-01 2.09005e-12 1.08665e-10 2 5.455987749722121e-01 5.455987749859126e-01 1.37005e-11 5.16431e-10 3 4.442688994717699e-01 4.442688994933023e-01 2.15324e-11 1.19299e-10 ----------------------------------------------------------------------------------------------------- 6 Ni 1 -9.822472224567664e-01 -9.822472224504862e-01 6.28020e-12 7.48338e-11 2 1.664135730143807e-01 1.664135729203000e-01 9.40807e-11 5.06285e-11 3 9.998890973691050e-01 9.998890974492569e-01 8.01519e-11 8.91478e-11 ----------------------------------------------------------------------------------------------------- 7 Cu 1 -4.984137079114087e-01 -4.984137079242084e-01 1.27998e-11 2.38733e-10 2 8.130642446945281e-01 8.130642446558314e-01 3.86967e-11 3.79602e-10 3 -1.479497833356282e-01 -1.479497833003573e-01 3.52709e-11 1.68608e-10 ----------------------------------------------------------------------------------------------------- 8 Ni 1 8.910202071485359e-01 8.910202071847743e-01 3.62383e-11 5.04937e-10 2 5.965778431765824e-01 5.965778432939328e-01 1.17350e-10 6.49360e-10 3 4.800015771940618e-01 4.800015772271076e-01 3.30458e-11 9.61733e-11 ----------------------------------------------------------------------------------------------------- 9 Ni 1 2.415950496709176e-02 2.415950495764023e-02 9.45153e-12 2.35344e-11 2 1.446775559529385e+00 1.446775559497794e+00 3.15912e-11 1.54970e-10 3 -1.144328861446732e+00 -1.144328861442981e+00 3.75189e-12 1.27910e-10 ----------------------------------------------------------------------------------------------------- 10 Cu 1 3.513315319179755e-01 3.513315319591640e-01 4.11885e-11 1.23757e-09 * 2 -5.651194241619417e-01 -5.651194241682570e-01 6.31528e-12 1.63548e-09 * 3 -3.686617840038943e-01 -3.686617839521175e-01 5.17769e-11 7.36547e-11 ----------------------------------------------------------------------------------------------------- 11 Ni 1 7.494193960705289e-02 7.494193960976096e-02 2.70807e-12 3.72866e-10 2 -2.522470566941864e+00 -2.522470566997166e+00 5.53015e-11 1.98169e-10 3 -2.420892816836978e+00 -2.420892816856773e+00 1.97948e-11 1.42922e-10 ----------------------------------------------------------------------------------------------------- 12 Ni 1 -1.723312393435319e+00 -1.723312393421233e+00 1.40865e-11 1.88359e-10 2 8.996306077744488e-01 8.996306077805265e-01 6.07769e-12 3.29843e-10 3 1.321299248884542e+00 1.321299248871996e+00 1.25464e-11 2.79049e-10 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -6.291669489446342e-01 -6.291669489298226e-01 1.48116e-11 6.29053e-11 2 -7.415426845516744e-01 -7.415426845557913e-01 4.11693e-12 6.42884e-11 3 2.702945996317159e-01 2.702945996397305e-01 8.01464e-12 1.77191e-10 ----------------------------------------------------------------------------------------------------- 14 Ni 1 -1.585390787998962e-02 -1.585390794784942e-02 6.78598e-11 4.95093e-11 2 4.932266175307581e-01 4.932266175107480e-01 2.00101e-11 1.17423e-10 3 3.996630183312767e-02 3.996630184100846e-02 7.88079e-12 1.17446e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 -4.847841971409848e-01 -4.847841971238122e-01 1.71727e-11 7.01316e-10 2 -4.353114346488788e-01 -4.353114346422606e-01 6.61815e-12 2.05050e-10 3 6.572699660312902e-01 6.572699660242394e-01 7.05080e-12 1.35478e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 1.901940111199256e+00 1.901940111189641e+00 9.61498e-12 4.61979e-11 2 3.479221498211185e-01 3.479221498357541e-01 1.46357e-11 2.00976e-09 * 3 -5.580336612959641e-01 -5.580336612684660e-01 2.74981e-11 2.60771e-10 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -9.734403585147062e-01 -9.734403585000182e-01 1.46880e-11 4.35871e-11 2 -1.336135867615669e+00 -1.336135867611165e+00 4.50329e-12 1.29320e-09 * 3 -1.577503604982231e+00 -1.577503604952847e+00 2.93843e-11 1.17919e-10 ----------------------------------------------------------------------------------------------------- 18 Ni 1 1.569415584050974e+00 1.569415583996512e+00 5.44613e-11 2.64997e-10 2 -5.629864212536598e-01 -5.629864212603800e-01 6.72018e-12 5.41726e-09 * 3 -4.480926133916514e-01 -4.480926133997700e-01 8.11862e-12 8.33676e-10 ----------------------------------------------------------------------------------------------------- 19 Cu 1 -2.804056734245805e+00 -2.804056734261982e+00 1.61768e-11 6.21760e-11 2 -3.443691208402324e+00 -3.443691208368208e+00 3.41154e-11 1.07091e-10 3 -2.158827872718885e-01 -2.158827872974639e-01 2.55754e-11 1.70639e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 -1.661952400449244e+00 -1.661952400427108e+00 2.21354e-11 2.71556e-10 2 -6.867936739111989e-02 -6.867936737326859e-02 1.78513e-11 1.50864e-10 3 1.690778697807630e+00 1.690778697798321e+00 9.30900e-12 3.88247e-11 ----------------------------------------------------------------------------------------------------- 21 Ni 1 1.084806345090245e+00 1.084806345051609e+00 3.86358e-11 1.69747e-10 2 8.090381112848291e-01 8.090381113018016e-01 1.69725e-11 1.70614e-10 3 6.093926720945469e-01 6.093926720953952e-01 8.48210e-13 3.50747e-11 ----------------------------------------------------------------------------------------------------- 22 Cu 1 -1.081258700409686e+00 -1.081258700409030e+00 6.56142e-13 1.37949e-10 2 -5.750059320884094e-01 -5.750059321241694e-01 3.57600e-11 4.45634e-10 3 3.736205858962418e-01 3.736205859414617e-01 4.52199e-11 3.78103e-10 ----------------------------------------------------------------------------------------------------- 23 Ni 1 -9.519183685954797e-01 -9.519183685914309e-01 4.04887e-12 2.21218e-10 2 8.138177567563057e-01 8.138177567656640e-01 9.35829e-12 2.23197e-10 3 -7.599480627594329e-01 -7.599480627559124e-01 3.52052e-12 1.04330e-10 ----------------------------------------------------------------------------------------------------- 24 Cu 1 3.832706574483777e+00 3.832706574477572e+00 6.20570e-12 9.93290e-11 2 3.232511089440287e+00 3.232511089420741e+00 1.95461e-11 1.44388e-10 3 -2.369028683678437e-01 -2.369028683459519e-01 2.18918e-11 1.31252e-10 ----------------------------------------------------------------------------------------------------- 25 Ni 1 3.972450117050079e-01 3.972450117072965e-01 2.28861e-12 2.52929e-09 * 2 1.348877610579729e+00 1.348877610579152e+00 5.76428e-13 3.48814e-10 3 -6.110111121803328e-01 -6.110111121984159e-01 1.80831e-11 2.63406e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -1.730012110614077e+00 -1.730012110682429e+00 6.83518e-11 1.34590e-09 * 2 7.986793452297810e-01 7.986793451846086e-01 4.51724e-11 3.43355e-11 3 1.654401094517231e+00 1.654401094574240e+00 5.70084e-11 1.92830e-10 ----------------------------------------------------------------------------------------------------- 27 Ni 1 1.178197994789083e+00 1.178197994807061e+00 1.79778e-11 4.59218e-10 2 1.559369039877642e+00 1.559369039869284e+00 8.35754e-12 3.44187e-10 3 -1.498516420060803e-01 -1.498516420324037e-01 2.63234e-11 5.13847e-10 ----------------------------------------------------------------------------------------------------- 28 Cu 1 5.465338841519715e-01 5.465338841533041e-01 1.33260e-12 7.94936e-10 2 -6.483642166007305e-01 -6.483642165884738e-01 1.22568e-11 1.32970e-10 3 -6.497910120879001e-01 -6.497910120956680e-01 7.76790e-12 2.52965e-10 ----------------------------------------------------------------------------------------------------- 29 Cu 1 2.469571687841082e+00 2.469571687710831e+00 1.30251e-10 1.13366e-09 * 2 -4.900883711924676e-01 -4.900883709229597e-01 2.69508e-10 3.28646e-10 3 9.530110345814715e-01 9.530110345565734e-01 2.48981e-11 1.38729e-10 ----------------------------------------------------------------------------------------------------- 30 Ni 1 -7.401680165524134e-01 -7.401680165841267e-01 3.17133e-11 2.96706e-10 2 -2.596328369603431e-01 -2.596328368865057e-01 7.38374e-11 2.62406e-10 3 -9.350163294608554e-01 -9.350163294741169e-01 1.32615e-11 5.15182e-10 ----------------------------------------------------------------------------------------------------- 31 Cu 1 -3.601184804426384e-01 -3.601184804457013e-01 3.06294e-12 8.20113e-11 2 -6.556103654887525e-01 -6.556103654890487e-01 2.96208e-13 2.20412e-10 3 -2.458523733376559e-01 -2.458523733084464e-01 2.92095e-11 4.07779e-10 ----------------------------------------------------------------------------------------------------- 32 Ni 1 -5.930880877292900e-01 -5.930880877505177e-01 2.12277e-11 2.96624e-10 2 -6.157215324481732e-01 -6.157215324576526e-01 9.47942e-12 3.10615e-11 3 -5.788480089203693e-01 -5.788480089340802e-01 1.37109e-11 1.92355e-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 = 14, direction = 1: |F_model - F_numer| error = ----------------------- = 4.28032e-09 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 4.28032e-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 4.28032e-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.