!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : SW_BereSerra_2006_GaN__MO_861114678890_000 Supported species : Ga N 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 = Ga | a0 = 3.72905445099 | (Configuration in file "config-Ga.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ga 1 1.040551232381957e+00 1.040551232382448e+00 4.90941e-13 3.69016e-12 2 -6.050285721321356e-02 -6.050285721245476e-02 7.58803e-13 2.99076e-12 3 -2.398917817705527e-01 -2.398917817704971e-01 5.56222e-14 3.09491e-12 ----------------------------------------------------------------------------------------------------- 2 Ga 1 -5.492510146108286e-01 -5.492510146107624e-01 6.61693e-14 9.71334e-13 2 3.715494449360633e-01 3.715494449343765e-01 1.68682e-12 5.17864e-12 3 1.522924546461131e+00 1.522924546462371e+00 1.24012e-12 1.06721e-11 ----------------------------------------------------------------------------------------------------- 3 Ga 1 6.268931265141059e-02 6.268931265342581e-02 2.01522e-12 2.30793e-10 * 2 1.162768076519449e+00 1.162768076517595e+00 1.85407e-12 1.78739e-11 3 -1.284081348321453e-01 -1.284081348311252e-01 1.02007e-12 7.32558e-12 ----------------------------------------------------------------------------------------------------- 4 Ga 1 1.134612692320744e+00 1.134612692319745e+00 9.98979e-13 2.09719e-11 2 9.538908174020623e-01 9.538908174048969e-01 2.83462e-12 1.31820e-11 3 8.397312321714232e-01 8.397312321708447e-01 5.78537e-13 3.33022e-12 ----------------------------------------------------------------------------------------------------- 5 Ga 1 2.697926264526238e-01 2.697926264532357e-01 6.11955e-13 2.30016e-12 2 6.687743710585068e-01 6.687743710555353e-01 2.97151e-12 3.53759e-11 3 8.468297068492081e-01 8.468297068492854e-01 7.72715e-14 3.48932e-12 ----------------------------------------------------------------------------------------------------- 6 Ga 1 -7.405161514789189e-01 -7.405161514795700e-01 6.51035e-13 6.03961e-12 2 -4.074896155145125e-01 -4.074896155155385e-01 1.02601e-12 1.74177e-12 3 5.181866317085475e-01 5.181866317070682e-01 1.47926e-12 1.40166e-12 ----------------------------------------------------------------------------------------------------- 7 Ga 1 8.058712173110877e-01 8.058712173093149e-01 1.77280e-12 5.02942e-12 2 -2.401414753230803e+00 -2.401414753230474e+00 3.28182e-13 9.66436e-11 * 3 -3.113225634238888e+00 -3.113225634238556e+00 3.31291e-13 5.37836e-12 ----------------------------------------------------------------------------------------------------- 8 Ga 1 -2.473821478798130e+00 -2.473821478799800e+00 1.67022e-12 3.42704e-12 2 -1.591088081880329e+00 -1.591088081880912e+00 5.82423e-13 1.08695e-11 3 -1.381452318136290e+00 -1.381452318133983e+00 2.30727e-12 1.63487e-11 ----------------------------------------------------------------------------------------------------- 9 Ga 1 1.087256395708560e+00 1.087256395708416e+00 1.44107e-13 9.90696e-12 2 -1.950514086145839e-01 -1.950514086148333e-01 2.49356e-13 4.04451e-12 3 1.063623498540283e+00 1.063623498537650e+00 2.63323e-12 9.88165e-12 ----------------------------------------------------------------------------------------------------- 10 Ga 1 -3.296872102654950e+00 -3.296872102655799e+00 8.49099e-13 8.77343e-12 2 9.137161391312935e-01 9.137161391291296e-01 2.16382e-12 4.52738e-12 3 -2.033955531901352e+00 -2.033955531900788e+00 5.63105e-13 2.65521e-12 ----------------------------------------------------------------------------------------------------- 11 Ga 1 -3.424202656249543e+00 -3.424202656248403e+00 1.13953e-12 4.37206e-12 2 -4.178270523253580e+00 -4.178270523250492e+00 3.08731e-12 7.85505e-12 3 -1.330835489611822e+00 -1.330835489611622e+00 2.00728e-13 2.42779e-11 ----------------------------------------------------------------------------------------------------- 12 Ga 1 4.485047616240957e-01 4.485047616224199e-01 1.67588e-12 8.39312e-12 2 -1.160598173004842e-01 -1.160598173002637e-01 2.20490e-13 1.10198e-11 3 -5.499490090400641e-01 -5.499490090406898e-01 6.25722e-13 3.72558e-12 ----------------------------------------------------------------------------------------------------- 13 Ga 1 5.962797253632172e-01 5.962797253634343e-01 2.17160e-13 3.53019e-11 2 -2.684919810800345e+00 -2.684919810798340e+00 2.00506e-12 4.38103e-11 3 -4.034377735145100e+00 -4.034377735146144e+00 1.04450e-12 9.49463e-12 ----------------------------------------------------------------------------------------------------- 14 Ga 1 -1.401613373566649e-01 -1.401613373562206e-01 4.44283e-13 9.24522e-12 2 3.077248192430621e-01 3.077248192428085e-01 2.53575e-13 1.79456e-12 3 -2.106192855508088e-01 -2.106192855496329e-01 1.17586e-12 2.62068e-12 ----------------------------------------------------------------------------------------------------- 15 Ga 1 2.933836949028204e+00 2.933836949025481e+00 2.72360e-12 1.81588e-12 2 3.805088330595394e-01 3.805088330611205e-01 1.58112e-12 2.28906e-12 3 1.116361104105392e+00 1.116361104110196e+00 4.80394e-12 6.54699e-12 ----------------------------------------------------------------------------------------------------- 16 Ga 1 2.731717870972245e+00 2.731717870969239e+00 3.00604e-12 2.99494e-12 2 4.882913906880430e+00 4.882913906880126e+00 3.03757e-13 1.32472e-11 3 1.501842180528270e+00 1.501842180527037e+00 1.23301e-12 2.44946e-11 ----------------------------------------------------------------------------------------------------- 17 Ga 1 6.944873378764101e-02 6.944873378789153e-02 2.50522e-13 1.39214e-11 2 4.337636140660127e-01 4.337636140645412e-01 1.47143e-12 2.66537e-12 3 -9.257257907006560e-01 -9.257257906970268e-01 3.62921e-12 1.26964e-11 ----------------------------------------------------------------------------------------------------- 18 Ga 1 4.678419451756316e-01 4.678419451798038e-01 4.17216e-12 2.02682e-12 2 2.051483556569939e+00 2.051483556573037e+00 3.09841e-12 9.46265e-12 3 -2.070996596302972e+00 -2.070996596302292e+00 6.80345e-13 4.39173e-11 ----------------------------------------------------------------------------------------------------- 19 Ga 1 1.295236266015125e-01 1.295236266007782e-01 7.34246e-13 3.38223e-10 * 2 -1.166429169799812e+00 -1.166429169797928e+00 1.88383e-12 4.02767e-12 3 7.846477344819618e-01 7.846477344815739e-01 3.87912e-13 7.00706e-12 ----------------------------------------------------------------------------------------------------- 20 Ga 1 1.834754693440239e-01 1.834754693446332e-01 6.09235e-13 8.30644e-12 2 4.016900517277774e-01 4.016900517261732e-01 1.60422e-12 3.18645e-12 3 -1.593465461646578e-01 -1.593465461642664e-01 3.91409e-13 5.64671e-12 ----------------------------------------------------------------------------------------------------- 21 Ga 1 -2.075521977465249e+00 -2.075521977462731e+00 2.51799e-12 4.47065e-12 2 -7.231871686234571e-01 -7.231871686195680e-01 3.88911e-12 1.30710e-11 3 1.323686310803552e+00 1.323686310805939e+00 2.38698e-12 2.66158e-11 ----------------------------------------------------------------------------------------------------- 22 Ga 1 1.753780531536050e+00 1.753780531540374e+00 4.32476e-12 9.40892e-12 2 2.538162414565422e+00 2.538162414563400e+00 2.02149e-12 3.84421e-11 3 2.754069913112796e+00 2.754069913112361e+00 4.35207e-13 2.77511e-12 ----------------------------------------------------------------------------------------------------- 23 Ga 1 -9.628458917600545e-01 -9.628458917610888e-01 1.03428e-12 4.39704e-12 2 7.767962711590746e-01 7.767962711601497e-01 1.07514e-12 1.04456e-11 3 -7.240695828841492e-01 -7.240695828833814e-01 7.67830e-13 6.36469e-12 ----------------------------------------------------------------------------------------------------- 24 Ga 1 1.191263218772764e+00 1.191263218770949e+00 1.81477e-12 1.71730e-10 * 2 4.136015965140025e-01 4.136015965050434e-01 8.95911e-12 1.47476e-11 3 -1.270257825520248e-03 -1.270257825325651e-03 1.94597e-13 2.87658e-12 ----------------------------------------------------------------------------------------------------- 25 Ga 1 -1.089060088601517e+00 -1.089060088601367e+00 1.50768e-13 9.08851e-12 2 -8.182588468541960e-01 -8.182588468548362e-01 6.40155e-13 1.49152e-10 * 3 6.013534891849825e-01 6.013534891821328e-01 2.84972e-12 4.70823e-12 ----------------------------------------------------------------------------------------------------- 26 Ga 1 -1.172554628035718e+00 -1.172554628032897e+00 2.82085e-12 2.21392e-11 2 2.936099677163788e+00 2.936099677160846e+00 2.94209e-12 1.52736e-11 3 4.023633745890435e-01 4.023633745912726e-01 2.22911e-12 1.39110e-11 ----------------------------------------------------------------------------------------------------- 27 Ga 1 6.724737064583928e-01 6.724737064654789e-01 7.08611e-12 1.45816e-11 2 -3.149517511413625e+00 -3.149517511415458e+00 1.83320e-12 6.41887e-12 3 6.718547265180179e-01 6.718547265180144e-01 3.55271e-15 1.97092e-11 ----------------------------------------------------------------------------------------------------- 28 Ga 1 -1.246097643977977e+00 -1.246097643981255e+00 3.27849e-12 1.97040e-11 2 8.596710446135188e-01 8.596710446125505e-01 9.68337e-13 1.78468e-12 3 -5.613184734918253e-02 -5.613184734853648e-02 6.46046e-13 1.44560e-11 ----------------------------------------------------------------------------------------------------- 29 Ga 1 4.718883987585218e-01 4.718883987606083e-01 2.08655e-12 2.15460e-11 2 -2.416099361065227e+00 -2.416099361061890e+00 3.33733e-12 6.38289e-12 3 1.756117450186028e+00 1.756117450185008e+00 1.01985e-12 1.42616e-10 * ----------------------------------------------------------------------------------------------------- 30 Ga 1 -6.788415920097024e-02 -6.788415920087772e-02 9.25232e-14 2.02415e-11 2 -1.747520468672449e-01 -1.747520468685053e-01 1.26038e-12 1.20204e-11 3 -5.180321537439496e-01 -5.180321537420260e-01 1.92357e-12 2.98839e-12 ----------------------------------------------------------------------------------------------------- 31 Ga 1 7.663227898789394e-01 7.663227898788371e-01 1.02363e-13 2.58769e-11 2 -1.168492133409144e+00 -1.168492133402757e+00 6.38667e-12 2.16429e-11 3 5.059090225358523e-01 5.059090225409889e-01 5.13656e-12 4.77951e-12 ----------------------------------------------------------------------------------------------------- 32 Ga 1 4.216579260628984e-01 4.216579260633475e-01 4.49141e-13 4.24427e-12 2 1.198418471230612e+00 1.198418471231415e+00 8.02913e-13 1.14073e-11 3 1.268786773421619e+00 1.268786773418761e+00 2.85816e-12 5.59965e-11 * ----------------------------------------------------------------------------------------------------- * 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 = 3: |F_model - F_numer| error = ----------------------- = 1.53194e-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 = N | a0 = 2.63598823547 | (Configuration in file "config-N.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 1.784689677067875e+00 1.784689677065949e+00 1.92579e-12 3.46145e-12 2 2.915347364092286e+00 2.915347364092963e+00 6.76792e-13 1.17573e-11 3 1.213323542396560e+00 1.213323542400227e+00 3.66684e-12 7.81730e-12 ----------------------------------------------------------------------------------------------------- 2 N 1 -2.134662094187857e+00 -2.134662094188967e+00 1.10978e-12 4.83360e-10 * 2 -6.922313926574689e-01 -6.922313926557234e-01 1.74549e-12 2.35219e-11 3 2.781717637190592e+00 2.781717637189760e+00 8.32223e-13 1.81584e-11 ----------------------------------------------------------------------------------------------------- 3 N 1 1.520168094160627e+00 1.520168094164990e+00 4.36318e-12 7.12295e-11 2 -5.588869691980561e-01 -5.588869691998155e-01 1.75937e-12 1.37724e-11 3 -4.574412933450331e-01 -4.574412933445811e-01 4.52027e-13 7.02303e-11 ----------------------------------------------------------------------------------------------------- 4 N 1 -2.892459941083554e-01 -2.892459941080519e-01 3.03590e-13 7.59748e-12 2 -9.116465913868012e-01 -9.116465913886244e-01 1.82321e-12 1.55304e-11 3 -3.951119374345133e+00 -3.951119374336509e+00 8.62466e-12 1.03242e-11 ----------------------------------------------------------------------------------------------------- 5 N 1 -4.102646368764216e+00 -4.102646368761754e+00 2.46114e-12 7.32392e-12 2 -8.023718120875479e-01 -8.023718120956014e-01 8.05345e-12 1.27431e-11 3 -2.009224068451087e+00 -2.009224068450797e+00 2.90434e-13 3.36708e-12 ----------------------------------------------------------------------------------------------------- 6 N 1 2.014007930054639e+00 2.014007930053876e+00 7.63833e-13 1.36247e-12 2 4.066066756703321e+00 4.066066756695883e+00 7.43761e-12 3.67884e-12 3 -4.552328991857761e+00 -4.552328991857306e+00 4.55636e-13 2.87373e-10 * ----------------------------------------------------------------------------------------------------- 7 N 1 3.905827720124289e+00 3.905827720127390e+00 3.10019e-12 3.15081e-12 2 -5.277409493009737e+00 -5.277409493008184e+00 1.55254e-12 5.98099e-12 3 3.441928649228239e+00 3.441928649226663e+00 1.57563e-12 2.01199e-11 ----------------------------------------------------------------------------------------------------- 8 N 1 -5.736044413373972e+00 -5.736044413374933e+00 9.61009e-13 1.08846e-11 2 5.421606984481424e+00 5.421606984481370e+00 5.41789e-14 5.58442e-11 3 4.935685368096512e+00 4.935685368097596e+00 1.08447e-12 1.49170e-11 ----------------------------------------------------------------------------------------------------- 9 N 1 3.058678193128522e+00 3.058678193129953e+00 1.43130e-12 1.23954e-11 2 1.702069450518018e-01 1.702069450543540e-01 2.55221e-12 3.17360e-12 3 9.505207908131921e-01 9.505207908067638e-01 6.42830e-12 8.95257e-11 ----------------------------------------------------------------------------------------------------- 10 N 1 -1.494997197908044e+00 -1.494997197903472e+00 4.57190e-12 9.09373e-11 2 -2.650081000013038e+00 -2.650081000012270e+00 7.67830e-13 8.57403e-12 3 2.640607156973334e+00 2.640607156974815e+00 1.48059e-12 6.64890e-12 ----------------------------------------------------------------------------------------------------- 11 N 1 2.244591371140904e+00 2.244591371146841e+00 5.93792e-12 2.51812e-11 2 1.190455299405856e+00 1.190455299401339e+00 4.51705e-12 1.16052e-11 3 -5.060671336060951e+00 -5.060671336066124e+00 5.17364e-12 1.01643e-11 ----------------------------------------------------------------------------------------------------- 12 N 1 2.322288359592366e+00 2.322288359592636e+00 2.70894e-13 1.15552e-12 2 -1.177814723033550e+00 -1.177814723033276e+00 2.74447e-13 1.72682e-11 3 -1.026447727592274e+00 -1.026447727591674e+00 5.99965e-13 9.16156e-12 ----------------------------------------------------------------------------------------------------- 13 N 1 -2.522231007996367e+00 -2.522231007978764e+00 1.76033e-11 4.91327e-11 2 -3.520493352025374e+00 -3.520493352031081e+00 5.70699e-12 2.89262e-11 3 -2.095075110307675e+00 -2.095075110301416e+00 6.25899e-12 6.35847e-12 ----------------------------------------------------------------------------------------------------- 14 N 1 1.364667207920231e+00 1.364667207922891e+00 2.66009e-12 5.88440e-12 2 3.494158186878414e+00 3.494158186877341e+00 1.07292e-12 8.29914e-12 3 -3.227028145349846e+00 -3.227028145351076e+00 1.23057e-12 4.19935e-11 ----------------------------------------------------------------------------------------------------- 15 N 1 5.337703508450796e+00 5.337703508451319e+00 5.23137e-13 4.19398e-12 2 -4.719967760170165e+00 -4.719967760174122e+00 3.95772e-12 2.71720e-11 3 5.909856110775014e-01 5.909856110873026e-01 9.80127e-12 8.35970e-11 ----------------------------------------------------------------------------------------------------- 16 N 1 -5.005628222417091e+00 -5.005628222415519e+00 1.57208e-12 1.94148e-10 * 2 2.411817696058870e+00 2.411817696065922e+00 7.05258e-12 7.20490e-12 3 1.063005442626277e+00 1.063005442644920e+00 1.86422e-11 9.75549e-11 ----------------------------------------------------------------------------------------------------- 17 N 1 -4.680699740269049e+00 -4.680699740271890e+00 2.84039e-12 1.27596e-11 2 -6.818394331815043e+00 -6.818394331812547e+00 2.49578e-12 3.74900e-12 3 -3.066340511588339e+00 -3.066340511587918e+00 4.20997e-13 7.28706e-12 ----------------------------------------------------------------------------------------------------- 18 N 1 4.247645087807278e+00 4.247645087810693e+00 3.41505e-12 1.27018e-11 2 5.415044285904781e-01 5.415044286000495e-01 9.57145e-12 2.33878e-11 3 -2.408267064996868e+00 -2.408267064989668e+00 7.20002e-12 3.34226e-11 ----------------------------------------------------------------------------------------------------- 19 N 1 4.605684952768170e+00 4.605684952764551e+00 3.61933e-12 2.49729e-11 2 -8.029164001962550e-01 -8.029164001898746e-01 6.38034e-12 7.74445e-11 3 1.545849375393068e+00 1.545849375389507e+00 3.56115e-12 8.05838e-11 ----------------------------------------------------------------------------------------------------- 20 N 1 -1.860071944458775e+00 -1.860071944455832e+00 2.94387e-12 8.29647e-12 2 3.578784553058659e+00 3.578784553062513e+00 3.85425e-12 5.25282e-11 3 4.696510745822520e+00 4.696510745820138e+00 2.38209e-12 1.35807e-10 * ----------------------------------------------------------------------------------------------------- 21 N 1 -3.877775559628335e+00 -3.877775559625750e+00 2.58416e-12 1.54405e-11 2 1.120478918829290e-01 1.120478918665734e-01 1.63556e-11 3.14545e-10 * 3 -5.430506534663164e+00 -5.430506534668631e+00 5.46763e-12 1.30056e-11 ----------------------------------------------------------------------------------------------------- 22 N 1 1.636255340190638e+00 1.636255340195895e+00 5.25713e-12 6.14953e-12 2 -3.753514054205345e+00 -3.753514054201520e+00 3.82494e-12 2.17697e-11 3 5.891485692879826e-01 5.891485692948960e-01 6.91336e-12 3.62063e-11 ----------------------------------------------------------------------------------------------------- 23 N 1 3.158428496559797e+00 3.158428496563672e+00 3.87468e-12 4.49019e-11 2 -2.969639045770689e-01 -2.969639045820230e-01 4.95415e-12 2.90656e-11 3 3.075519681403686e+00 3.075519681403610e+00 7.59393e-14 1.62625e-11 ----------------------------------------------------------------------------------------------------- 24 N 1 -6.635872443736965e-01 -6.635872443735580e-01 1.38556e-13 4.10164e-10 * 2 2.531875612609553e+00 2.531875612620067e+00 1.05138e-11 1.35327e-11 3 4.236934022532848e-01 4.236934022537628e-01 4.78007e-13 4.70206e-11 ----------------------------------------------------------------------------------------------------- 25 N 1 -4.292813461724468e+00 -4.292813461721943e+00 2.52509e-12 3.54916e-12 2 2.663411078025951e+00 2.663411078030775e+00 4.82370e-12 1.80953e-11 3 1.007663793796059e-01 1.007663793786809e-01 9.25079e-13 3.12224e-11 ----------------------------------------------------------------------------------------------------- 26 N 1 2.907228902404489e+00 2.907228902403939e+00 5.50227e-13 1.30864e-11 2 2.327783174351716e+00 2.327783174357072e+00 5.35572e-12 1.44693e-11 3 4.234990919780524e-01 4.234990919749572e-01 3.09519e-12 1.49214e-11 ----------------------------------------------------------------------------------------------------- 27 N 1 2.956409047488415e+00 2.956409047496890e+00 8.47544e-12 1.24181e-11 2 7.462460621954022e-01 7.462460622001966e-01 4.79439e-12 4.57629e-11 3 3.926979823064905e+00 3.926979823066998e+00 2.09299e-12 4.63451e-12 ----------------------------------------------------------------------------------------------------- 28 N 1 1.029616561948280e+00 1.029616561944849e+00 3.43148e-12 5.99873e-11 2 -9.302823124501863e-01 -9.302823124492726e-01 9.13714e-13 7.41773e-12 3 -1.494302649592737e+00 -1.494302649596695e+00 3.95795e-12 1.66993e-11 ----------------------------------------------------------------------------------------------------- 29 N 1 -3.744963109780568e+00 -3.744963109778958e+00 1.60938e-12 2.22942e-11 2 2.264188843933228e+00 2.264188843934682e+00 1.45439e-12 2.36482e-10 * 3 3.709466195028621e+00 3.709466195026191e+00 2.43006e-12 2.19380e-12 ----------------------------------------------------------------------------------------------------- 30 N 1 -2.175060852006453e-01 -2.175060851995128e-01 1.13251e-12 9.67137e-12 2 1.220843130779587e+00 1.220843130782010e+00 2.42273e-12 3.78919e-12 3 2.428911308815122e+00 2.428911308808571e+00 6.55120e-12 1.98983e-11 ----------------------------------------------------------------------------------------------------- 31 N 1 -2.813750350417475e+00 -2.813750350421946e+00 4.47153e-12 2.19744e-11 2 5.683609001186825e-01 5.683609001186561e-01 2.63123e-14 7.43849e-12 3 -1.841611219554892e+00 -1.841611219553443e+00 1.44840e-12 3.02558e-11 ----------------------------------------------------------------------------------------------------- 32 N 1 -6.572676561984119e-01 -6.572676561970522e-01 1.35969e-12 9.32066e-12 2 -3.311730811392532e+00 -3.311730811391260e+00 1.27187e-12 2.90612e-12 3 -1.917754743123307e+00 -1.917754743128173e+00 4.86566e-12 2.08831e-11 ----------------------------------------------------------------------------------------------------- * 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 = 18, direction = 2: |F_model - F_numer| error = ----------------------- = 1.76757e-11 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 = Ga N | a0 = 3.37634940246 | (Configuration in file "config-GaN.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ga 1 2.826676127471610e+00 2.826676127470842e+00 7.67830e-13 8.16280e-12 2 6.916413746151510e-01 6.916413746164917e-01 1.34071e-12 3.27172e-12 3 7.287228140662463e-01 7.287228140671373e-01 8.91065e-13 7.12308e-12 ----------------------------------------------------------------------------------------------------- 2 N 1 -4.373355065088150e-01 -4.373355065053445e-01 3.47050e-12 1.42691e-11 2 -5.860620309246423e-01 -5.860620309315712e-01 6.92890e-12 3.57809e-11 3 -4.589097703772723e-01 -4.589097703750240e-01 2.24826e-12 3.29664e-11 ----------------------------------------------------------------------------------------------------- 3 N 1 2.687672286936376e+00 2.687672286941063e+00 4.68736e-12 1.49365e-11 2 -5.393885542719075e+00 -5.393885542719743e+00 6.67910e-13 5.22959e-12 3 -2.590100694420456e+00 -2.590100694425453e+00 4.99734e-12 2.95546e-11 ----------------------------------------------------------------------------------------------------- 4 Ga 1 -1.301296062163181e+01 -1.301296062163100e+01 8.06466e-13 3.62554e-12 2 -8.857843129009001e-01 -8.857843129038545e-01 2.95441e-12 2.15840e-11 3 -1.010214846418327e+01 -1.010214846418492e+01 1.65201e-12 1.32037e-11 ----------------------------------------------------------------------------------------------------- 5 N 1 2.555332265363589e+00 2.555332265362873e+00 7.15428e-13 1.65863e-11 2 1.250803869264634e+00 1.250803869269323e+00 4.68869e-12 5.61018e-12 3 1.657091708978849e+00 1.657091708980457e+00 1.60827e-12 3.29825e-12 ----------------------------------------------------------------------------------------------------- 6 Ga 1 1.304193542336914e+00 1.304193542337721e+00 8.07576e-13 2.64069e-11 2 -4.312154105926762e-01 -4.312154105922684e-01 4.07785e-13 1.88354e-11 3 -1.329864749671777e+00 -1.329864749672858e+00 1.08047e-12 3.10862e-12 ----------------------------------------------------------------------------------------------------- 7 Ga 1 5.007939154681393e+00 5.007939154684006e+00 2.61391e-12 5.26867e-12 2 -5.475596995289209e+00 -5.475596995288437e+00 7.71827e-13 6.80789e-12 3 -5.915164778067350e+00 -5.915164778070475e+00 3.12550e-12 1.21005e-11 ----------------------------------------------------------------------------------------------------- 8 N 1 -3.398316832131338e+00 -3.398316832131735e+00 3.97460e-13 1.41990e-10 * 2 6.131031328910577e-01 6.131031328941532e-01 3.09552e-12 1.84752e-11 3 -6.860710387085245e-01 -6.860710387097776e-01 1.25311e-12 8.24663e-12 ----------------------------------------------------------------------------------------------------- 9 N 1 -1.170694160683193e+00 -1.170694160686043e+00 2.85039e-12 1.38018e-11 2 -5.446551810233930e-02 -5.446551810197382e-02 3.65485e-13 1.07485e-11 3 -1.987883769855282e-01 -1.987883769874435e-01 1.91527e-12 1.67218e-11 ----------------------------------------------------------------------------------------------------- 10 N 1 -5.657903771319165e+00 -5.657903771319251e+00 8.61533e-14 9.54792e-12 2 3.827746276590050e+00 3.827746276590054e+00 3.99680e-15 1.34248e-12 3 -3.592385658809936e+00 -3.592385658808884e+00 1.05160e-12 1.20837e-11 ----------------------------------------------------------------------------------------------------- 11 Ga 1 -1.296254973684137e+00 -1.296254973684733e+00 5.96634e-13 3.17835e-12 2 6.148437468097039e-01 6.148437468119865e-01 2.28262e-12 1.59004e-11 3 1.464204171858557e-02 1.464204172596760e-02 7.38203e-12 1.14415e-11 ----------------------------------------------------------------------------------------------------- 12 Ga 1 5.236108700751814e-02 5.236108701124487e-02 3.72673e-12 4.37654e-12 2 5.799690527516320e-01 5.799690527476399e-01 3.99214e-12 2.39625e-11 3 -3.102944481794730e-01 -3.102944481736121e-01 5.86092e-12 2.23406e-11 ----------------------------------------------------------------------------------------------------- 13 Ga 1 -1.840646361302865e+00 -1.840646361302888e+00 2.35367e-14 9.26925e-12 2 -7.233226006762103e+00 -7.233226006763980e+00 1.87672e-12 9.23972e-12 3 -9.539951975099621e+00 -9.539951975102277e+00 2.65565e-12 1.75859e-12 ----------------------------------------------------------------------------------------------------- 14 Ga 1 3.037693581196612e+00 3.037693581198422e+00 1.81055e-12 3.08464e-12 2 1.373534438652560e+00 1.373534438652800e+00 2.39364e-13 1.08915e-11 3 -1.273299368823836e+00 -1.273299368822951e+00 8.85292e-13 5.80913e-12 ----------------------------------------------------------------------------------------------------- 15 N 1 7.209106999676115e+00 7.209106999677483e+00 1.36868e-12 1.50342e-11 2 -1.548326027804607e+00 -1.548326027800086e+00 4.52105e-12 2.38076e-12 3 4.676292403868521e-01 4.676292403857396e-01 1.11250e-12 1.06823e-11 ----------------------------------------------------------------------------------------------------- 16 Ga 1 -1.169675995331429e-01 -1.169675995319410e-01 1.20191e-12 6.46865e-12 2 1.362758914570643e+01 1.362758914570582e+01 6.05738e-13 1.12337e-11 3 2.497599600394965e+00 2.497599600397965e+00 3.00027e-12 2.05493e-11 ----------------------------------------------------------------------------------------------------- 17 N 1 -9.172034959984421e-01 -9.172034960067770e-01 8.33489e-12 9.50159e-11 * 2 -3.628359356675827e+00 -3.628359356675260e+00 5.67102e-13 6.04228e-12 3 4.354560461899157e+00 4.354560461899350e+00 1.92735e-13 2.29168e-11 ----------------------------------------------------------------------------------------------------- 18 Ga 1 1.095622145277763e+01 1.095622145277814e+01 5.11591e-13 3.56160e-11 2 9.515123657106147e-01 9.515123657049154e-01 5.69933e-12 2.89578e-11 3 9.877993374748836e+00 9.877993374749948e+00 1.11200e-12 8.39506e-11 * ----------------------------------------------------------------------------------------------------- 19 Ga 1 6.424621993634657e-01 6.424621993587343e-01 4.73144e-12 1.08776e-11 2 -2.941992123748091e+00 -2.941992123747387e+00 7.03881e-13 1.53388e-11 3 -1.443176406805596e+00 -1.443176406807326e+00 1.72995e-12 3.44540e-11 ----------------------------------------------------------------------------------------------------- 20 Ga 1 -1.379130440346657e+00 -1.379130440344164e+00 2.49334e-12 2.03475e-11 2 4.029730250493724e+00 4.029730250494737e+00 1.01252e-12 3.10774e-12 3 4.400436687410128e-01 4.400436687392200e-01 1.79279e-12 9.46460e-12 ----------------------------------------------------------------------------------------------------- 21 Ga 1 -9.826228326470941e+00 -9.826228326472517e+00 1.57563e-12 1.17790e-11 2 -8.382177566305414e+00 -8.382177566306778e+00 1.36424e-12 2.22347e-11 3 -5.882516470177218e-01 -5.882516470190851e-01 1.36324e-12 1.27041e-11 ----------------------------------------------------------------------------------------------------- 22 Ga 1 7.017845643744692e+00 7.017845643748795e+00 4.10338e-12 1.20428e-11 2 1.082240921233949e+01 1.082240921234352e+01 4.02878e-12 2.52900e-11 3 -3.298223892948026e+00 -3.298223892947023e+00 1.00364e-12 9.32232e-12 ----------------------------------------------------------------------------------------------------- 23 N 1 3.431941559462682e+00 3.431941559463338e+00 6.56808e-13 5.51603e-12 2 -3.959118375861114e+00 -3.959118375861902e+00 7.87370e-13 7.87947e-12 3 3.445052802343243e+00 3.445052802343658e+00 4.15668e-13 8.51008e-12 ----------------------------------------------------------------------------------------------------- 24 Ga 1 -6.989902043412674e+00 -6.989902043413615e+00 9.40581e-13 6.70575e-12 2 6.295941913709590e+00 6.295941913713733e+00 4.14335e-12 7.68186e-12 3 8.153409904792243e+00 8.153409904792152e+00 9.05942e-14 3.53957e-11 ----------------------------------------------------------------------------------------------------- 25 N 1 -4.281639091814261e+00 -4.281639091812727e+00 1.53477e-12 8.24052e-12 2 3.422132462581767e+00 3.422132462579776e+00 1.99085e-12 8.98748e-12 3 2.727268596579122e+00 2.727268596581565e+00 2.44249e-12 8.70859e-12 ----------------------------------------------------------------------------------------------------- 26 N 1 -3.161296871136847e-01 -3.161296871102178e-01 3.46689e-12 2.50566e-11 2 6.422973439399393e-01 6.422973439411257e-01 1.18638e-12 1.31969e-11 3 3.891453264020636e-01 3.891453264000705e-01 1.99307e-12 3.75803e-11 ----------------------------------------------------------------------------------------------------- 27 N 1 -1.007987851005760e-01 -1.007987851006560e-01 8.00332e-14 3.53546e-12 2 -2.558808498899644e+00 -2.558808498899464e+00 1.79856e-13 3.32490e-12 3 -1.994480941856552e-01 -1.994480941906764e-01 5.02118e-12 1.09845e-10 * ----------------------------------------------------------------------------------------------------- 28 N 1 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 2 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 3 0.000000000000000e+00 0.000000000000000e+00 0.00000e+00 0.00000e+00 ----------------------------------------------------------------------------------------------------- 29 N 1 1.632700959604788e+00 1.632700959605816e+00 1.02784e-12 8.12239e-13 2 -4.300619403293029e+00 -4.300619403289417e+00 3.61222e-12 3.71942e-11 3 4.831448098364326e+00 4.831448098369179e+00 4.85390e-12 2.75016e-11 ----------------------------------------------------------------------------------------------------- 30 Ga 1 1.863734490944919e+00 1.863734490947448e+00 2.52842e-12 5.09015e-12 2 9.316763315811923e-02 9.316763315897936e-02 8.60131e-13 4.04325e-11 3 3.803115118735132e+00 3.803115118734931e+00 2.00728e-13 1.78613e-12 ----------------------------------------------------------------------------------------------------- 31 N 1 -4.929117185952145e-01 -4.929117185933169e-01 1.89765e-12 3.31195e-11 2 -1.381459741513122e+00 -1.381459741518345e+00 5.22338e-12 1.03679e-11 3 -1.057169179933488e+00 -1.057169179934551e+00 1.06293e-12 1.12044e-11 ----------------------------------------------------------------------------------------------------- 32 N 1 1.009142065078608e+00 1.009142065089830e+00 1.12226e-11 2.15696e-11 2 -7.532530782267151e-02 -7.532530782173387e-02 9.37639e-13 1.17201e-11 3 -8.044742139330980e-01 -8.044742139330424e-01 5.56222e-14 1.62870e-12 ----------------------------------------------------------------------------------------------------- * 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 = 11, direction = 3: |F_model - F_numer| error = ----------------------- = 5.04167e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 5.04167e-10 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 5.04167e-10 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.