!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : EAM_Dynamo_BorovikovMendelevKing_2016_CuZr__MO_097471813275_000 Supported species : Cu Zr 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 = 3.63856887817 | (Configuration in file "config-Cu.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 1.998719920197952e-01 1.998719920248240e-01 5.02878e-12 1.97835e-10 2 -2.748644722478315e-02 -2.748644716673390e-02 5.80493e-11 9.83962e-10 3 -3.096895280370834e-01 -3.096895280306939e-01 6.38956e-12 8.44901e-09 * ----------------------------------------------------------------------------------------------------- 2 Cu 1 -4.276971093304373e-01 -4.276971094039120e-01 7.34747e-11 4.93672e-10 2 9.657871646113939e-01 9.657871645548647e-01 5.65292e-11 4.98973e-10 3 8.559319307102682e-01 8.559319307721064e-01 6.18382e-11 3.03505e-10 ----------------------------------------------------------------------------------------------------- 3 Cu 1 2.910598135679481e-01 2.910598135364660e-01 3.14820e-11 1.70572e-10 2 6.656844883930247e-01 6.656844882694385e-01 1.23586e-10 5.96353e-10 3 9.161629044803415e-01 9.161629045488507e-01 6.85092e-11 3.08293e-10 ----------------------------------------------------------------------------------------------------- 4 Cu 1 8.311184297968569e-01 8.311184297729908e-01 2.38661e-11 5.79550e-10 2 4.689830023518073e-01 4.689830024528987e-01 1.01091e-10 9.84320e-11 3 7.625012946287736e-01 7.625012946026136e-01 2.61600e-11 2.96572e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 5.018191458784764e-01 5.018191458897522e-01 1.12758e-11 1.19038e-10 2 1.067547942785645e-01 1.067547943832875e-01 1.04723e-10 8.44477e-10 3 3.173033247262799e-01 3.173033248127760e-01 8.64961e-11 1.45141e-10 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -8.245691269863143e-01 -8.245691270056346e-01 1.93202e-11 4.92181e-10 2 5.650449569251023e-01 5.650449567760922e-01 1.49010e-10 9.43873e-10 3 7.704070880098068e-01 7.704070880128182e-01 3.01137e-12 1.40979e-10 ----------------------------------------------------------------------------------------------------- 7 Cu 1 3.826357010708625e-01 3.826357010555640e-01 1.52985e-11 6.31568e-10 2 -1.553068566744091e+00 -1.553068566748616e+00 4.52571e-12 6.08753e-11 3 -1.802811138877374e+00 -1.802811138817531e+00 5.98430e-11 2.46373e-10 ----------------------------------------------------------------------------------------------------- 8 Cu 1 -1.609061544300096e+00 -1.609061544281032e+00 1.90647e-11 3.48052e-10 2 -1.178134141964408e+00 -1.178134142005174e+00 4.07656e-11 4.97968e-10 3 -7.663961400801688e-01 -7.663961401271606e-01 4.69919e-11 4.07271e-10 ----------------------------------------------------------------------------------------------------- 9 Cu 1 1.433651031138562e-01 1.433651030469989e-01 6.68573e-11 9.70325e-10 2 -1.799954810114057e+00 -1.799954810014506e+00 9.95515e-11 4.22735e-10 3 -1.767627080897069e+00 -1.767627080822629e+00 7.44407e-11 2.69230e-10 ----------------------------------------------------------------------------------------------------- 10 Cu 1 -3.847570498620168e-01 -3.847570498706746e-01 8.65785e-12 2.25260e-10 2 2.413376645070318e-01 2.413376644424641e-01 6.45677e-11 2.50817e-10 3 -5.093995521473464e-01 -5.093995520809876e-01 6.63588e-11 1.02254e-10 ----------------------------------------------------------------------------------------------------- 11 Cu 1 -1.533484331298475e-01 -1.533484332977148e-01 1.67867e-10 7.08769e-10 2 -1.170695477175438e+00 -1.170695477239697e+00 6.42595e-11 7.37332e-11 3 8.121504309006569e-01 8.121504307387496e-01 1.61907e-10 1.07880e-09 ----------------------------------------------------------------------------------------------------- 12 Cu 1 1.181232650185173e-01 1.181232650558889e-01 3.73716e-11 1.65446e-10 2 1.325038980535542e+00 1.325038980509272e+00 2.62697e-11 2.22828e-10 3 1.811323170955101e+00 1.811323170797910e+00 1.57191e-10 1.20819e-10 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -6.682896114433687e-01 -6.682896112837911e-01 1.59578e-10 4.19604e-10 2 -1.305285099499805e+00 -1.305285099530045e+00 3.02403e-11 2.99920e-10 3 -1.476260769936308e+00 -1.476260769982757e+00 4.64486e-11 1.29993e-09 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -2.303428047681398e-01 -2.303428048201339e-01 5.19941e-11 2.42375e-10 2 2.970736121299368e-01 2.970736121022519e-01 2.76849e-11 1.85783e-10 3 2.221255113243001e-01 2.221255113406945e-01 1.63944e-11 6.50163e-10 ----------------------------------------------------------------------------------------------------- 15 Cu 1 1.631543128155243e+00 1.631543128312709e+00 1.57466e-10 8.93095e-10 2 -6.834129292270015e-01 -6.834129292291499e-01 2.14839e-12 3.65039e-10 3 7.405408319037133e-01 7.405408319580223e-01 5.43090e-11 9.39495e-10 ----------------------------------------------------------------------------------------------------- 16 Cu 1 9.637864891468814e-01 9.637864890700121e-01 7.68693e-11 3.62465e-09 * 2 1.235385836432050e+00 1.235385836463589e+00 3.15392e-11 5.99675e-10 3 8.215175727537808e-01 8.215175726852939e-01 6.84869e-11 1.96784e-10 ----------------------------------------------------------------------------------------------------- 17 Cu 1 -8.006784425041190e-01 -8.006784424506154e-01 5.35036e-11 2.73694e-10 2 -1.595952413098197e-01 -1.595952412896667e-01 2.01530e-11 1.12254e-10 3 -1.077296502486561e+00 -1.077296502603221e+00 1.16660e-10 1.06236e-10 ----------------------------------------------------------------------------------------------------- 18 Cu 1 1.276461480459154e+00 1.276461480375386e+00 8.37681e-11 1.42608e-10 2 1.665095842816824e+00 1.665095842697401e+00 1.19422e-10 1.58070e-09 3 -9.022114729131707e-01 -9.022114734683420e-01 5.55171e-10 7.10644e-10 ----------------------------------------------------------------------------------------------------- 19 Cu 1 9.529300381832592e-01 9.529300382277394e-01 4.44802e-11 4.59787e-10 2 -7.902188619724491e-01 -7.902188621374135e-01 1.64964e-10 6.62425e-10 3 8.231564281044021e-01 8.231564283221449e-01 2.17743e-10 9.85983e-10 ----------------------------------------------------------------------------------------------------- 20 Cu 1 2.441689687620133e-01 2.441689688038479e-01 4.18346e-11 5.21732e-10 2 8.955473214477503e-01 8.955473215157342e-01 6.79840e-11 5.92550e-10 3 -1.599575659752223e-01 -1.599575660358371e-01 6.06148e-11 4.78634e-11 ----------------------------------------------------------------------------------------------------- 21 Cu 1 -1.215550536230624e+00 -1.215550536256211e+00 2.55864e-11 3.69610e-10 2 3.341224535074830e-01 3.341224533939863e-01 1.13497e-10 2.28021e-10 3 2.347496960662113e-01 2.347496959972435e-01 6.89677e-11 2.27223e-09 ----------------------------------------------------------------------------------------------------- 22 Cu 1 3.261823591363603e-01 3.261823590206137e-01 1.15747e-10 2.12032e-10 2 2.281395555185511e+00 2.281395555278181e+00 9.26699e-11 1.12366e-09 3 1.806552415063620e+00 1.806552415144524e+00 8.09044e-11 5.79844e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -4.559324241058463e-01 -4.559324241259798e-01 2.01335e-11 2.26524e-09 2 4.465481983350044e-01 4.465481982983134e-01 3.66910e-11 2.02691e-10 3 -2.958225466753697e-01 -2.958225467429403e-01 6.75706e-11 2.70029e-10 ----------------------------------------------------------------------------------------------------- 24 Cu 1 1.440920448239469e-01 1.440920449035051e-01 7.95583e-11 3.87746e-10 2 4.306607477186121e-01 4.306607479381163e-01 2.19504e-10 3.39818e-10 3 -1.127944415333027e+00 -1.127944415300900e+00 3.21265e-11 3.93819e-10 ----------------------------------------------------------------------------------------------------- 25 Cu 1 -5.116747706811929e-01 -5.116747706806105e-01 5.82423e-13 7.27651e-10 2 -1.056824678186558e+00 -1.056824678076203e+00 1.10355e-10 3.04789e-09 * 3 -9.652294603005525e-01 -9.652294603839464e-01 8.33940e-11 2.82282e-10 ----------------------------------------------------------------------------------------------------- 26 Cu 1 -9.985451514607737e-01 -9.985451521814431e-01 7.20669e-10 1.14525e-09 2 6.077946750836742e-01 6.077946750198159e-01 6.38584e-11 3.23027e-09 * 3 -1.226947811180803e+00 -1.226947811374848e+00 1.94045e-10 1.18778e-09 ----------------------------------------------------------------------------------------------------- 27 Cu 1 1.239314070244284e+00 1.239314070365176e+00 1.20893e-10 7.24251e-10 2 -2.476143158288230e+00 -2.476143158343301e+00 5.50706e-11 4.54121e-09 * 3 4.691725929130416e-01 4.691725928020386e-01 1.11003e-10 1.11610e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 -7.029406215670424e-01 -7.029406213348867e-01 2.32156e-10 1.39482e-09 2 1.126737038448735e+00 1.126737038597610e+00 1.48875e-10 9.32081e-10 3 9.745964956956268e-02 9.745964957578132e-02 6.21864e-12 5.71783e-10 ----------------------------------------------------------------------------------------------------- 29 Cu 1 -9.318419723365258e-01 -9.318419721511494e-01 1.85376e-10 4.57252e-09 * 2 -1.276394820440833e+00 -1.276394820603462e+00 1.62629e-10 2.83963e-10 3 2.450131176418562e-01 2.450131176673287e-01 2.54725e-11 4.64991e-10 ----------------------------------------------------------------------------------------------------- 30 Cu 1 -5.363607622827643e-01 -5.363607622296270e-01 5.31373e-11 5.12826e-10 2 4.766737218971914e-01 4.766737218572343e-01 3.99571e-11 2.12895e-10 3 -6.553530279481038e-01 -6.553530279135450e-01 3.45588e-11 3.80521e-10 ----------------------------------------------------------------------------------------------------- 31 Cu 1 5.340920727300054e-01 5.340920727085614e-01 2.14440e-11 9.66519e-11 2 -1.468385565658593e+00 -1.468385565524029e+00 1.34565e-10 7.60496e-10 3 5.754573837257462e-01 5.754573836303948e-01 9.53514e-11 5.17423e-10 ----------------------------------------------------------------------------------------------------- 32 Cu 1 6.710262588816509e-01 6.710262586593480e-01 2.22303e-10 1.60109e-09 2 8.099337432008271e-01 8.099337432270306e-01 2.62035e-11 5.90750e-09 * 3 7.614216693106973e-01 7.614216693916845e-01 8.09872e-11 1.63473e-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 dicontinuities. Maximum error obtained for particle = 1, direction = 2: |F_model - F_numer| error = ----------------------- = 2.11192e-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 = Zr | a0 = 4.54452390671 | (Configuration in file "config-Zr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Zr 1 5.050900289219543e-01 5.050900289066492e-01 1.53051e-11 1.33499e-09 2 7.629679820780635e-02 7.629679802180188e-02 1.86004e-10 9.26707e-11 3 8.262853573499133e-02 8.262853579359358e-02 5.86022e-11 2.13625e-10 ----------------------------------------------------------------------------------------------------- 2 Zr 1 5.895088302206133e-01 5.895088306159587e-01 3.95345e-10 9.36785e-11 2 -3.365536279757851e-01 -3.365536282555511e-01 2.79766e-10 7.66325e-09 * 3 -7.322758153018261e-01 -7.322758153869839e-01 8.51579e-11 9.12167e-10 ----------------------------------------------------------------------------------------------------- 3 Zr 1 7.860248029222181e-01 7.860248028479998e-01 7.42183e-11 3.31183e-10 2 -1.756530162112168e-01 -1.756530162448525e-01 3.36356e-11 3.80517e-10 3 1.631162544200493e-01 1.631162544460970e-01 2.60477e-11 5.13578e-10 ----------------------------------------------------------------------------------------------------- 4 Zr 1 -2.910184072051902e-01 -2.910184072758405e-01 7.06503e-11 4.75672e-10 2 9.832074936325523e-01 9.832074934838385e-01 1.48714e-10 1.34065e-09 3 2.912185633329674e-01 2.912185634256543e-01 9.26869e-11 4.34791e-10 ----------------------------------------------------------------------------------------------------- 5 Zr 1 -1.236522500014292e-01 -1.236522499119277e-01 8.95016e-11 9.36968e-10 2 1.280451429837846e+00 1.280451430064164e+00 2.26318e-10 2.68281e-10 3 8.554697763710127e-01 8.554697764422237e-01 7.12109e-11 8.03908e-10 ----------------------------------------------------------------------------------------------------- 6 Zr 1 -1.951432812593722e-01 -1.951432812884427e-01 2.90705e-11 3.06092e-10 2 -5.081476168669306e-01 -5.081476168567917e-01 1.01389e-11 2.74288e-10 3 1.817063109479325e-01 1.817063110703031e-01 1.22371e-10 2.20022e-10 ----------------------------------------------------------------------------------------------------- 7 Zr 1 -1.875670008050197e-01 -1.875670009305057e-01 1.25486e-10 9.53063e-12 2 4.601673032242517e-01 4.601673033581142e-01 1.33863e-10 1.33429e-09 3 2.064340560847028e-01 2.064340563418660e-01 2.57163e-10 9.98983e-10 ----------------------------------------------------------------------------------------------------- 8 Zr 1 -8.239157950563287e-01 -8.239157950799323e-01 2.36036e-11 4.52665e-10 2 3.586447859953470e-02 3.586447898020852e-02 3.80674e-10 9.39398e-10 3 6.846962227669992e-01 6.846962225891059e-01 1.77893e-10 3.62428e-10 ----------------------------------------------------------------------------------------------------- 9 Zr 1 6.828301746209283e-01 6.828301747027806e-01 8.18523e-11 2.24148e-11 2 -5.530167209697616e-01 -5.530167212387396e-01 2.68978e-10 1.29911e-09 3 9.618501242489866e-01 9.618501240355046e-01 2.13482e-10 1.86527e-09 ----------------------------------------------------------------------------------------------------- 10 Zr 1 -1.479403860766060e+00 -1.479403860710124e+00 5.59364e-11 1.06415e-09 2 5.220841042537496e-01 5.220841042394666e-01 1.42830e-11 8.95542e-10 3 -3.662893689590898e-01 -3.662893690353948e-01 7.63050e-11 2.80850e-10 ----------------------------------------------------------------------------------------------------- 11 Zr 1 5.547651712172568e-01 5.547651712359001e-01 1.86433e-11 4.24106e-10 2 1.503360165818103e-01 1.503360165654807e-01 1.63296e-11 2.61314e-10 3 2.576862052001306e-01 2.576862050850933e-01 1.15037e-10 2.09831e-10 ----------------------------------------------------------------------------------------------------- 12 Zr 1 6.839840113110043e-01 6.839840114026425e-01 9.16383e-11 1.84373e-09 2 -2.726955032899439e-01 -2.726955033246405e-01 3.46966e-11 6.18825e-10 3 -2.316766419619297e-01 -2.316766420616664e-01 9.97367e-11 1.50147e-10 ----------------------------------------------------------------------------------------------------- 13 Zr 1 3.549700703268129e-01 3.549700702330866e-01 9.37263e-11 9.30934e-10 2 -1.484282092218396e+00 -1.484282091571698e+00 6.46698e-10 4.40036e-10 3 -1.006710700035985e+00 -1.006710700214298e+00 1.78313e-10 4.80140e-10 ----------------------------------------------------------------------------------------------------- 14 Zr 1 -1.507027456962715e-01 -1.507027456864582e-01 9.81334e-12 1.22413e-11 2 -6.768880391300084e-01 -6.768880390910327e-01 3.89757e-11 3.02499e-10 3 7.113393047399100e-01 7.113393047631327e-01 2.32226e-11 3.54901e-10 ----------------------------------------------------------------------------------------------------- 15 Zr 1 -1.634741758784405e-01 -1.634741760015176e-01 1.23077e-10 4.63174e-10 2 4.159817664584067e-01 4.159817662992604e-01 1.59146e-10 8.49008e-10 3 -5.132732392168573e-01 -5.132732392457392e-01 2.88819e-11 7.45572e-10 ----------------------------------------------------------------------------------------------------- 16 Zr 1 3.492429142873405e-01 3.492429143319370e-01 4.45965e-11 3.17979e-09 * 2 8.332881820717473e-01 8.332881820471834e-01 2.45639e-11 1.56437e-09 3 1.973077861773064e+00 1.973077861554762e+00 2.18301e-10 9.94853e-11 ----------------------------------------------------------------------------------------------------- 17 Zr 1 5.707775466648239e-01 5.707775466770969e-01 1.22730e-11 6.49951e-10 2 2.815024710930176e-01 2.815024711164554e-01 2.34378e-11 2.23172e-10 3 5.350481132312079e-01 5.350481131661941e-01 6.50139e-11 3.75705e-10 ----------------------------------------------------------------------------------------------------- 18 Zr 1 5.105516298080183e-01 5.105516298170221e-01 9.00380e-12 1.62500e-09 2 5.955621957981202e-01 5.955621957550867e-01 4.30335e-11 3.07991e-10 3 6.671783569641416e-01 6.671783571336671e-01 1.69526e-10 3.98485e-10 ----------------------------------------------------------------------------------------------------- 19 Zr 1 -8.268699839502071e-02 -8.268699841565279e-02 2.06321e-11 3.61171e-10 2 1.118528626227567e+00 1.118528626217384e+00 1.01825e-11 8.84085e-10 3 -1.158184731568403e+00 -1.158184731541764e+00 2.66391e-11 6.70196e-10 ----------------------------------------------------------------------------------------------------- 20 Zr 1 5.354786035729627e-01 5.354786033876032e-01 1.85360e-10 3.15549e-10 2 -6.634967253082272e-01 -6.634967251949506e-01 1.13277e-10 5.54812e-10 3 -6.556605710202037e-01 -6.556605711107566e-01 9.05529e-11 3.93032e-10 ----------------------------------------------------------------------------------------------------- 21 Zr 1 -6.887884475766677e-01 -6.887884474850077e-01 9.16600e-11 2.80624e-10 2 7.595319306755320e-02 7.595319300245390e-02 6.50993e-11 6.35547e-10 3 -6.766341831689084e-01 -6.766341830025042e-01 1.66404e-10 4.43811e-09 * ----------------------------------------------------------------------------------------------------- 22 Zr 1 -2.667276432243834e-02 -2.667276429815181e-02 2.42865e-11 2.80971e-10 2 -7.504812282551672e-01 -7.504812281781186e-01 7.70486e-11 5.11245e-10 3 -5.648573262291918e-01 -5.648573263736956e-01 1.44504e-10 2.67179e-09 * ----------------------------------------------------------------------------------------------------- 23 Zr 1 -2.526279999216715e-01 -2.526279997942762e-01 1.27395e-10 1.82004e-10 2 5.162475560026615e-01 5.162475559650703e-01 3.75912e-11 5.77673e-10 3 -3.339466774842562e-01 -3.339466775372515e-01 5.29953e-11 3.24898e-10 ----------------------------------------------------------------------------------------------------- 24 Zr 1 -9.750826866278357e-01 -9.750826866633885e-01 3.55528e-11 8.79452e-10 2 5.166819052891680e-01 5.166819052802532e-01 8.91487e-12 3.34157e-10 3 2.968500434119591e-01 2.968500434253432e-01 1.33841e-11 4.55798e-10 ----------------------------------------------------------------------------------------------------- 25 Zr 1 -1.195255584641607e+00 -1.195255584749371e+00 1.07764e-10 4.23248e-10 2 -5.208630082083977e-01 -5.208630079218682e-01 2.86529e-10 1.33909e-10 3 9.986812568596751e-01 9.986812569651000e-01 1.05425e-10 3.92378e-10 ----------------------------------------------------------------------------------------------------- 26 Zr 1 1.185507617945390e+00 1.185507618012773e+00 6.73834e-11 8.41651e-10 2 7.505323302214654e-01 7.505323301841962e-01 3.72692e-11 5.48419e-10 3 -8.770967808595913e-01 -8.770967808526673e-01 6.92402e-12 8.73237e-10 ----------------------------------------------------------------------------------------------------- 27 Zr 1 1.122754917845011e+00 1.122754917824356e+00 2.06550e-11 2.95257e-10 2 -5.135865522186169e-01 -5.135865523357334e-01 1.17116e-10 7.25499e-10 3 -4.233466899902831e-01 -4.233466902272129e-01 2.36930e-10 6.15701e-10 ----------------------------------------------------------------------------------------------------- 28 Zr 1 4.650355394060507e-02 4.650355426748020e-02 3.26875e-10 5.73288e-10 2 -6.523738534150757e-01 -6.523738534242131e-01 9.13736e-12 8.69584e-11 3 -3.473326457054423e-01 -3.473326457783416e-01 7.28992e-11 9.59338e-11 ----------------------------------------------------------------------------------------------------- 29 Zr 1 -8.458793988577608e-01 -8.458793994908848e-01 6.33124e-10 4.49510e-10 2 -7.245170848811493e-01 -7.245170850419687e-01 1.60819e-10 3.60821e-10 3 -4.233953651547855e-01 -4.233953651045231e-01 5.02625e-11 7.05155e-10 ----------------------------------------------------------------------------------------------------- 30 Zr 1 -4.846231975454020e-01 -4.846231975738522e-01 2.84502e-11 3.48540e-10 2 -5.665050129845767e-01 -5.665050127251616e-01 2.59415e-10 5.06154e-10 3 2.877830745086318e-01 2.877830740749230e-01 4.33709e-10 4.78724e-10 ----------------------------------------------------------------------------------------------------- 31 Zr 1 -3.672772211284603e-01 -3.672772209772411e-01 1.51219e-10 4.92602e-10 2 3.499802513997201e-01 3.499802512828178e-01 1.16902e-10 1.32391e-10 3 -2.967592322645325e-01 -2.967592323240300e-01 5.94975e-11 5.62325e-11 ----------------------------------------------------------------------------------------------------- 32 Zr 1 -1.442180579199620e-01 -1.442180579736738e-01 5.37118e-11 7.97261e-10 2 -5.636060200337250e-01 -5.636060198931342e-01 1.40591e-10 3.19028e-10 3 -5.473240916750765e-01 -5.473240917807364e-01 1.05660e-10 1.91365e-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 dicontinuities. Maximum error obtained for particle = 8, direction = 2: |F_model - F_numer| error = ----------------------- = 1.06142e-08 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 Zr | a0 = 3.96067946479 | (Configuration in file "config-CuZr.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Cu 1 8.719717171089707e-01 8.719717171164005e-01 7.42983e-12 4.58747e-10 2 8.202411368563364e-01 8.202411368225541e-01 3.37823e-11 8.32826e-10 3 9.682333511033318e-01 9.682333511425310e-01 3.91992e-11 2.90918e-10 ----------------------------------------------------------------------------------------------------- 2 Zr 1 -5.197643486493220e-01 -5.197643484966618e-01 1.52660e-10 8.57338e-10 2 -4.077206243723473e-01 -4.077206244125731e-01 4.02258e-11 3.82505e-09 3 -4.441597463666407e-01 -4.441597460938717e-01 2.72769e-10 5.01134e-10 ----------------------------------------------------------------------------------------------------- 3 Zr 1 -1.617839288081491e+00 -1.617839288199527e+00 1.18036e-10 5.26919e-10 2 -3.581481387609509e-01 -3.581481387587100e-01 2.24087e-12 6.14151e-10 3 -4.607739807390046e+00 -4.607739807422309e+00 3.22631e-11 9.33378e-10 ----------------------------------------------------------------------------------------------------- 4 Cu 1 4.366877768367989e-01 4.366877768105118e-01 2.62871e-11 3.54844e-09 2 -8.939393972037030e-01 -8.939393971414711e-01 6.22319e-11 1.53307e-08 * 3 -7.270730681574632e-01 -7.270730679833163e-01 1.74147e-10 2.90432e-10 ----------------------------------------------------------------------------------------------------- 5 Cu 1 -6.888267832760440e+00 -6.888267832739109e+00 2.13314e-11 1.29979e-10 2 -3.198097287576599e-01 -3.198097287287796e-01 2.88803e-11 1.51318e-09 3 -4.903732997496439e+00 -4.903732997500117e+00 3.67795e-12 1.38879e-09 ----------------------------------------------------------------------------------------------------- 6 Cu 1 -3.671202451988358e-01 -3.671202452499155e-01 5.10798e-11 6.58987e-10 2 1.617255658885551e+00 1.617255659019866e+00 1.34315e-10 1.43383e-09 3 -4.630656843222723e-01 -4.630656842232602e-01 9.90121e-11 1.77387e-09 ----------------------------------------------------------------------------------------------------- 7 Zr 1 6.474544149572211e+00 6.474544149633871e+00 6.16600e-11 7.49358e-10 2 -1.358570125485494e+00 -1.358570125587032e+00 1.01538e-10 1.48854e-09 3 6.059436590910577e+00 6.059436591079016e+00 1.68439e-10 1.81170e-09 ----------------------------------------------------------------------------------------------------- 8 Zr 1 -1.457265663659195e+00 -1.457265664457840e+00 7.98645e-10 2.26139e-09 2 7.581587151653426e-01 7.581587151718282e-01 6.48559e-12 5.11821e-10 3 -1.069104689355970e+00 -1.069104689623680e+00 2.67709e-10 1.11617e-09 ----------------------------------------------------------------------------------------------------- 9 Zr 1 -9.254359103599694e-01 -9.254359104629817e-01 1.03012e-10 4.86069e-10 2 -6.858473193351758e-01 -6.858473191516818e-01 1.83494e-10 4.13367e-10 3 1.774225583243610e-01 1.774225582109544e-01 1.13407e-10 3.58783e-10 ----------------------------------------------------------------------------------------------------- 10 Zr 1 8.198721527622175e-01 8.198721528494750e-01 8.72575e-11 8.19228e-09 * 2 8.643053217041321e-01 8.643053218715774e-01 1.67445e-10 2.10771e-10 3 -1.223406419805650e+00 -1.223406419986826e+00 1.81176e-10 1.03221e-09 ----------------------------------------------------------------------------------------------------- 11 Cu 1 5.175272781553431e-01 5.175272783806513e-01 2.25308e-10 1.12351e-09 2 -1.416973171359791e+00 -1.416973171557719e+00 1.97927e-10 9.56399e-11 3 6.571509359949822e-01 6.571509360575711e-01 6.25889e-11 8.44183e-10 ----------------------------------------------------------------------------------------------------- 12 Cu 1 -1.311006516608426e-02 -1.311006521677597e-02 5.06917e-11 3.25697e-10 2 8.776225700849312e-02 8.776225706261249e-02 5.41194e-11 3.83769e-10 3 2.371374022958066e-01 2.371374022909597e-01 4.84693e-12 2.03168e-10 ----------------------------------------------------------------------------------------------------- 13 Cu 1 -3.323943245033882e-01 -3.323943241459208e-01 3.57467e-10 1.03473e-09 2 -8.183539880522555e-01 -8.183539880040250e-01 4.82304e-11 8.78471e-09 * 3 7.352677117956818e-01 7.352677117995857e-01 3.90388e-12 3.14173e-10 ----------------------------------------------------------------------------------------------------- 14 Cu 1 -1.472169816864807e-01 -1.472169817565722e-01 7.00914e-11 5.14467e-10 2 3.309880098920295e-01 3.309880098168438e-01 7.51857e-11 5.71993e-10 3 7.781076711953182e-01 7.781076712696694e-01 7.43512e-11 7.77254e-10 ----------------------------------------------------------------------------------------------------- 15 Zr 1 9.205417414074092e-01 9.205417416406855e-01 2.33276e-10 1.48268e-10 2 -2.139704297162413e+00 -2.139704297102645e+00 5.97673e-11 1.37692e-09 3 -4.845639541368992e+00 -4.845639540875724e+00 4.93268e-10 1.37378e-09 ----------------------------------------------------------------------------------------------------- 16 Cu 1 9.476850943792431e-01 9.476850943925994e-01 1.33563e-11 5.07963e-10 2 -1.834073007932240e-01 -1.834073016590106e-01 8.65787e-10 2.74519e-09 3 7.550859174757879e-02 7.550859176283105e-02 1.52523e-11 3.50642e-10 ----------------------------------------------------------------------------------------------------- 17 Zr 1 -1.313975656041981e+00 -1.313975655883573e+00 1.58408e-10 2.44716e-09 2 4.978963318906662e-01 4.978963316847272e-01 2.05939e-10 8.93643e-10 3 1.560356984599824e+00 1.560356984658432e+00 5.86073e-11 3.19896e-10 ----------------------------------------------------------------------------------------------------- 18 Cu 1 9.142402451803311e-01 9.142402452133435e-01 3.30124e-11 2.96272e-10 2 2.546123545509221e-01 2.546123546576597e-01 1.06738e-10 7.50061e-10 3 5.794629595729692e-01 5.794629592203959e-01 3.52573e-10 1.47216e-09 ----------------------------------------------------------------------------------------------------- 19 Cu 1 -4.117048448766109e-01 -4.117048448021543e-01 7.44566e-11 6.00715e-10 2 1.446368086201106e-01 1.446368087157386e-01 9.56280e-11 1.30420e-09 3 -9.707913942632047e-01 -9.707913942766062e-01 1.34015e-11 1.20048e-10 ----------------------------------------------------------------------------------------------------- 20 Zr 1 9.291265438303479e-01 9.291265436365883e-01 1.93760e-10 1.29724e-09 2 1.352146153660007e-01 1.352146154177984e-01 5.17977e-11 2.41457e-10 3 -8.883061738400473e-01 -8.883061739499397e-01 1.09892e-10 2.82775e-10 ----------------------------------------------------------------------------------------------------- 21 Cu 1 2.924160288651546e+00 2.924160288433234e+00 2.18312e-10 1.01220e-09 2 6.384974659666348e-01 6.384974660245969e-01 5.79621e-11 1.26901e-09 3 3.267116087812663e+00 3.267116087711881e+00 1.00782e-10 5.79812e-10 ----------------------------------------------------------------------------------------------------- 22 Zr 1 9.819130168651601e-01 9.819130169057262e-01 4.05661e-11 1.52853e-10 2 -1.762384630669378e+00 -1.762384630869588e+00 2.00210e-10 8.61810e-10 3 2.763723512858118e+00 2.763723512904323e+00 4.62048e-11 6.43652e-10 ----------------------------------------------------------------------------------------------------- 23 Cu 1 -7.238486941703739e-01 -7.238486941253025e-01 4.50714e-11 2.70765e-10 2 9.203082763884922e-01 9.203082764301643e-01 4.16721e-11 4.02492e-10 3 -8.763617434731350e-01 -8.763617434027672e-01 7.03678e-11 5.22828e-10 ----------------------------------------------------------------------------------------------------- 24 Cu 1 6.194585128306387e-01 6.194585128492293e-01 1.85906e-11 6.80197e-10 2 -3.630529900514878e-04 -3.630522168717994e-04 7.73180e-10 3.30464e-10 3 -1.083806070604953e+00 -1.083806070375017e+00 2.29936e-10 5.08108e-10 ----------------------------------------------------------------------------------------------------- 25 Zr 1 -9.081937777350702e-01 -9.081937777017177e-01 3.33524e-11 8.02987e-10 2 -1.363278296162448e-02 -1.363278289260762e-02 6.90169e-11 1.94083e-09 3 4.717687089231820e-02 4.717687086576662e-02 2.65516e-11 1.01566e-09 ----------------------------------------------------------------------------------------------------- 26 Zr 1 -3.330755545393726e+00 -3.330755544988672e+00 4.05053e-10 5.53700e-09 * 2 1.360667330194456e+00 1.360667330093734e+00 1.00721e-10 3.28202e-10 3 -2.427828762349673e+00 -2.427828761913525e+00 4.36148e-10 3.36465e-10 ----------------------------------------------------------------------------------------------------- 27 Cu 1 3.925039781636137e-01 3.925039783498179e-01 1.86204e-10 1.49225e-09 2 6.208528063495232e-01 6.208528062666563e-01 8.28669e-11 3.39881e-10 3 8.619198077609647e-01 8.619198077619553e-01 9.90652e-13 3.63497e-09 ----------------------------------------------------------------------------------------------------- 28 Cu 1 6.383847789318674e-01 6.383847789665945e-01 3.47271e-11 7.20760e-11 2 -6.329004418054234e-01 -6.329004418797358e-01 7.43124e-11 6.14437e-10 3 -3.491016310538624e-01 -3.491016310824185e-01 2.85562e-11 3.73224e-10 ----------------------------------------------------------------------------------------------------- 29 Zr 1 -1.846963426727909e+00 -1.846963426573959e+00 1.53950e-10 2.74587e-10 2 -1.795663592750555e+00 -1.795663592790920e+00 4.03655e-11 1.17026e-09 3 6.625477805559254e-02 6.625477799496882e-02 6.06237e-11 1.62973e-09 ----------------------------------------------------------------------------------------------------- 30 Zr 1 8.733387123891763e-01 8.733387125280349e-01 1.38859e-10 2.27509e-10 2 4.046990550126043e+00 4.046990549600152e+00 5.25890e-10 1.40783e-09 3 2.044924476717878e+00 2.044924476819642e+00 1.01764e-10 1.50299e-09 ----------------------------------------------------------------------------------------------------- 31 Zr 1 5.727492292314895e-02 5.727492292357991e-02 4.30961e-13 3.85452e-10 2 -1.116128119040336e+00 -1.116128119040484e+00 1.47216e-13 5.27409e-10 3 2.593624984004542e-01 2.593624982864683e-01 1.13986e-10 3.70224e-10 ----------------------------------------------------------------------------------------------------- 32 Zr 1 1.484625695022854e+00 1.484625694900019e+00 1.22835e-10 5.29857e-09 * 2 8.051590725356488e-01 8.051590725069073e-01 2.87415e-11 2.95400e-10 3 3.741554939809931e+00 3.741554939338350e+00 4.71581e-10 1.38681e-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 dicontinuities. Maximum error obtained for particle = 24, direction = 2: |F_model - F_numer| error = ----------------------- = 2.12967e-06 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 2.12967e-06 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: B Comment: The letter grade B was assigned because the normalized error in the computation was 2.12967e-06 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.