!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-periodicity-support !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check that the model supports periodic boundary conditions correctly. If the simulation box is increased by an integer factor along a periodic direction, the total energy must multiply by that factor and the forces on atoms that are periodic copies of each other must be the same. The check is performed for a randomly distorted non-periodic face-centered cubic (FCC) cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. For each configuration, all possible combinations of periodic boundary conditions are tested: TFF, FTF, FFT, TTF, TFT, TTF, TTT (where 'T' indicates periodicity along a direction, and 'F' indicates no periodicity). The verification check passes if the energy of all configurations that the model is able to compute support all periodic boundary conditions correctly. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------ Results for KIM Model : EAM_Dynamo_MendelevSrolovitzAckland_2005_AlFe__MO_577453891941_005 Supported species : Al Fe random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTT (Configuration in file "config-Al-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.14740710435 2^p V(r_1,...,r_N) = -5.14740710435 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -5.11539009e+00 -8.74710854e+00 -9.60171219e+00 | -5.11539009e+00 -8.74710854e+00 -9.60171219e+00 1 3.46280310e+00 2.47282569e+00 -2.07303098e+00 | 3.46280310e+00 2.47282569e+00 -2.07303098e+00 2 4.36592464e+00 -3.29006005e+00 4.75369110e+00 | 4.36592464e+00 -3.29006005e+00 4.75369110e+00 3 -2.71333765e+00 9.56434291e+00 6.92105207e+00 | -2.71333765e+00 9.56434291e+00 6.92105207e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTF (Configuration in file "config-Al-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.24212556979 2^p V(r_1,...,r_N) = -3.24212556979 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.47195612e+00 -5.10266947e+00 -4.78238428e+00 | -7.47195612e+00 -5.10266947e+00 -4.78238428e+00 1 5.39973344e+00 4.43167568e+00 -6.73649554e+00 | 5.39973344e+00 4.43167568e+00 -6.73649554e+00 2 9.63700964e+00 -1.04456340e+01 8.49954606e+00 | 9.63700964e+00 -1.04456340e+01 8.49954606e+00 3 -7.56478696e+00 1.11166278e+01 3.01933376e+00 | -7.56478696e+00 1.11166278e+01 3.01933376e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFT (Configuration in file "config-Al-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.826213121987 2^p V(r_1,...,r_N) = -0.826213121987 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.71089750e+00 -1.03712525e+01 -1.30788303e+01 | -7.71089750e+00 -1.03712525e+01 -1.30788303e+01 1 1.03413121e+01 1.04310847e+01 -5.99870303e+00 | 1.03413121e+01 1.04310847e+01 -5.99870303e+00 2 6.46320595e+00 -8.77508100e+00 9.43330691e+00 | 6.46320595e+00 -8.77508100e+00 9.43330691e+00 3 -9.09362052e+00 8.71524887e+00 9.64422644e+00 | -9.09362052e+00 8.71524887e+00 9.64422644e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFF (Configuration in file "config-Al-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 7.64623385253 2^p V(r_1,...,r_N) = 7.64623385253 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.67285565e+01 -1.48288138e+01 -2.68367635e+01 | -1.67285565e+01 -1.48288138e+01 -2.68367635e+01 1 8.79258094e+00 1.08775016e+01 -7.12100838e+00 | 8.79258094e+00 1.08775016e+01 -7.12100838e+00 2 2.05585750e+01 -1.21843152e+01 2.08160327e+01 | 2.05585750e+01 -1.21843152e+01 2.08160327e+01 3 -1.26225995e+01 1.61356273e+01 1.31417392e+01 | -1.26225995e+01 1.61356273e+01 1.31417392e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTT (Configuration in file "config-Al-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.18218867105 2^p V(r_1,...,r_N) = -1.18218867105 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.06743713e+01 -7.55967958e+00 -1.03226750e+01 | -1.06743713e+01 -7.55967958e+00 -1.03226750e+01 1 7.07154374e+00 9.38510832e+00 -7.88487206e+00 | 7.07154374e+00 9.38510832e+00 -7.88487206e+00 2 1.02014846e+01 -1.07512469e+01 9.48795988e+00 | 1.02014846e+01 -1.07512469e+01 9.48795988e+00 3 -6.59865706e+00 8.92581815e+00 8.71958714e+00 | -6.59865706e+00 8.92581815e+00 8.71958714e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTF (Configuration in file "config-Al-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.06221135794 2^p V(r_1,...,r_N) = -5.06221135794 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.37162629e+00 -6.86658253e+00 -4.89566980e+00 | -8.37162629e+00 -6.86658253e+00 -4.89566980e+00 1 4.94703507e+00 6.89177480e+00 -5.53143979e+00 | 4.94703507e+00 6.89177480e+00 -5.53143979e+00 2 5.90973375e+00 -3.20215691e+00 8.53556405e+00 | 5.90973375e+00 -3.20215691e+00 8.53556405e+00 3 -2.48514253e+00 3.17696464e+00 1.89154554e+00 | -2.48514253e+00 3.17696464e+00 1.89154554e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FFT (Configuration in file "config-Al-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 5.61494455803 2^p V(r_1,...,r_N) = 5.61494455803 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.78389881e+00 -7.98038931e+00 -1.06588315e+01 | -8.78389881e+00 -7.98038931e+00 -1.06588315e+01 1 1.12975469e+01 1.11213866e+01 -9.20572169e+00 | 1.12975469e+01 1.11213866e+01 -9.20572169e+00 2 1.99880591e+01 -2.30560998e+01 1.26224494e+01 | 1.99880591e+01 -2.30560998e+01 1.26224494e+01 3 -2.25017071e+01 1.99151025e+01 7.24210377e+00 | -2.25017071e+01 1.99151025e+01 7.24210377e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TTT (Configuration in file "config-Fe-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.23835236693 2^p V(r_1,...,r_N) = -4.23835236693 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.95069867e+00 -3.58589329e+00 -8.93700615e+00 | -7.95069867e+00 -3.58589329e+00 -8.93700615e+00 1 3.06210570e+00 5.44832966e+00 -4.13079470e+00 | 3.06210570e+00 5.44832966e+00 -4.13079470e+00 2 1.10855538e+01 -7.96280972e+00 9.47217820e+00 | 1.10855538e+01 -7.96280972e+00 9.47217820e+00 3 -6.19696079e+00 6.10037335e+00 3.59562265e+00 | -6.19696079e+00 6.10037335e+00 3.59562265e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TTF (Configuration in file "config-Fe-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.05488692338 2^p V(r_1,...,r_N) = -3.05488692338 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -5.64232872e+00 -3.94152333e+00 -4.61535710e+00 | -5.64232872e+00 -3.94152333e+00 -4.61535710e+00 1 4.06558671e+00 6.71475754e+00 -5.71801328e+00 | 4.06558671e+00 6.71475754e+00 -5.71801328e+00 2 1.54080480e+01 -1.41448506e+01 6.34615489e+00 | 1.54080480e+01 -1.41448506e+01 6.34615489e+00 3 -1.38313060e+01 1.13716163e+01 3.98721549e+00 | -1.38313060e+01 1.13716163e+01 3.98721549e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TFT (Configuration in file "config-Fe-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.68929534879 2^p V(r_1,...,r_N) = -6.68929534879 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -9.37037204e-01 -1.43468811e+00 -1.20331869e+00 | -9.37037204e-01 -1.43468811e+00 -1.20331869e+00 1 1.86860197e+00 3.99540071e+00 -7.08782293e+00 | 1.86860197e+00 3.99540071e+00 -7.08782293e+00 2 1.92416100e+00 -5.92330367e+00 7.09500745e+00 | 1.92416100e+00 -5.92330367e+00 7.09500745e+00 3 -2.85572577e+00 3.36259108e+00 1.19613416e+00 | -2.85572577e+00 3.36259108e+00 1.19613416e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = TFF (Configuration in file "config-Fe-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.72394989531 2^p V(r_1,...,r_N) = -5.72394989531 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.13394701e+00 -1.09444518e+01 -9.57878193e+00 | -2.13394701e+00 -1.09444518e+01 -9.57878193e+00 1 1.65032136e+00 1.98229319e+00 -2.41738780e+00 | 1.65032136e+00 1.98229319e+00 -2.41738780e+00 2 1.38484771e+00 -2.30262817e+00 2.32108727e+00 | 1.38484771e+00 -2.30262817e+00 2.32108727e+00 3 -9.01222061e-01 1.12647867e+01 9.67508245e+00 | -9.01222061e-01 1.12647867e+01 9.67508245e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FTT (Configuration in file "config-Fe-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -8.12947798321 2^p V(r_1,...,r_N) = -8.12947798321 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.33717168e-02 -7.16534939e-01 -9.15349515e-01 | -8.33717168e-02 -7.16534939e-01 -9.15349515e-01 1 1.23828371e+00 2.82469899e-01 -1.44399077e+00 | 1.23828371e+00 2.82469899e-01 -1.44399077e+00 2 1.39596572e+00 -1.83195203e+00 3.56334039e-01 | 1.39596572e+00 -1.83195203e+00 3.56334039e-01 3 -2.55087772e+00 2.26601707e+00 2.00300625e+00 | -2.55087772e+00 2.26601707e+00 2.00300625e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FTF (Configuration in file "config-Fe-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.31872086859 2^p V(r_1,...,r_N) = -3.31872086859 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -6.08670978e+00 -7.33030759e+00 -2.44503863e+00 | -6.08670978e+00 -7.33030759e+00 -2.44503863e+00 1 6.69417276e+00 6.21115317e+00 -3.37239804e+00 | 6.69417276e+00 6.21115317e+00 -3.37239804e+00 2 1.34710346e+01 -1.45567583e+01 4.14883935e+00 | 1.34710346e+01 -1.45567583e+01 4.14883935e+00 3 -1.40784976e+01 1.56759127e+01 1.66859732e+00 | -1.40784976e+01 1.56759127e+01 1.66859732e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Fe, PBC = FFT (Configuration in file "config-Fe-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.90018248055 2^p V(r_1,...,r_N) = -7.90018248055 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.35924574e+00 -2.61068706e+00 -2.74308946e+00 | -1.35924574e+00 -2.61068706e+00 -2.74308946e+00 1 9.65216531e-01 5.93979087e-01 2.81481112e-02 | 9.65216531e-01 5.93979087e-01 2.81481112e-02 2 1.34240120e+00 -1.19258747e+00 5.34058983e-01 | 1.34240120e+00 -1.19258747e+00 5.34058983e-01 3 -9.48371996e-01 3.20929544e+00 2.18088236e+00 | -9.48371996e-01 3.20929544e+00 2.18088236e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Fe, PBC = TTT (Configuration in file "config-AlFe-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.24259012638 2^p V(r_1,...,r_N) = -7.24259012638 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -9.77297046e-01 -1.39697642e+00 -2.69716854e+00 | -9.77297046e-01 -1.39697642e+00 -2.69716854e+00 1 -3.40035593e-01 1.85760080e+00 -1.88172542e+00 | -3.40035593e-01 1.85760080e+00 -1.88172542e+00 2 2.81479701e+00 -3.15883298e+00 2.31220058e+00 | 2.81479701e+00 -3.15883298e+00 2.31220058e+00 3 -1.49746437e+00 2.69820860e+00 2.26669339e+00 | -1.49746437e+00 2.69820860e+00 2.26669339e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Fe, PBC = TTF (Configuration in file "config-AlFe-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.66814201837 2^p V(r_1,...,r_N) = -1.66814201837 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.14987897e+01 -1.41462661e+01 -8.06451195e+00 | -1.14987897e+01 -1.41462661e+01 -8.06451195e+00 1 1.44209646e+01 9.73028766e+00 -7.09158732e+00 | 1.44209646e+01 9.73028766e+00 -7.09158732e+00 2 3.39311665e+00 -4.07748937e+00 4.66398994e+00 | 3.39311665e+00 -4.07748937e+00 4.66398994e+00 3 -6.31529154e+00 8.49346785e+00 1.04921093e+01 | -6.31529154e+00 8.49346785e+00 1.04921093e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Fe, PBC = TFT (Configuration in file "config-AlFe-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.113229798863 2^p V(r_1,...,r_N) = 0.113229798863 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.65173603e+00 -1.42129534e+01 -1.42154995e+01 | -8.65173603e+00 -1.42129534e+01 -1.42154995e+01 1 1.47201636e+01 4.96330407e+00 -1.36235295e+01 | 1.47201636e+01 4.96330407e+00 -1.36235295e+01 2 5.78984497e+00 -4.67443840e+00 3.43926947e+00 | 5.78984497e+00 -4.67443840e+00 3.43926947e+00 3 -1.18582725e+01 1.39240877e+01 2.43997595e+01 | -1.18582725e+01 1.39240877e+01 2.43997595e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Fe, PBC = TFF (Configuration in file "config-AlFe-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.12449446045 2^p V(r_1,...,r_N) = -6.12449446045 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -3.92687721e+00 -4.32521277e+00 -1.51809118e+00 | -3.92687721e+00 -4.32521277e+00 -1.51809118e+00 1 5.84231555e+00 4.31285612e+00 -4.05266588e+00 | 5.84231555e+00 4.31285612e+00 -4.05266588e+00 2 1.63577912e+00 -1.99681475e+00 2.76856890e-01 | 1.63577912e+00 -1.99681475e+00 2.76856890e-01 3 -3.55121746e+00 2.00917140e+00 5.29390017e+00 | -3.55121746e+00 2.00917140e+00 5.29390017e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Fe, PBC = FTT (Configuration in file "config-AlFe-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1.13820741042 2^p V(r_1,...,r_N) = 1.13820741042 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -5.44784693e+00 -9.96355949e+00 -8.42386538e+00 | -5.44784693e+00 -9.96355949e+00 -8.42386538e+00 1 2.53929308e+01 8.56847679e+00 -1.69940443e+01 | 2.53929308e+01 8.56847679e+00 -1.69940443e+01 2 1.89492991e+00 -5.85885488e+00 4.93797853e+00 | 1.89492991e+00 -5.85885488e+00 4.93797853e+00 3 -2.18400138e+01 7.25393758e+00 2.04799311e+01 | -2.18400138e+01 7.25393758e+00 2.04799311e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Fe, PBC = FTF (Configuration in file "config-AlFe-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.08852749966 2^p V(r_1,...,r_N) = -4.08852749966 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -6.12609565e+00 -6.91386335e+00 -3.59812712e+00 | -6.12609565e+00 -6.91386335e+00 -3.59812712e+00 1 7.00137170e+00 9.29611814e+00 -1.09705412e+01 | 7.00137170e+00 9.29611814e+00 -1.09705412e+01 2 3.83446273e+00 -7.30945987e+00 9.74466150e+00 | 3.83446273e+00 -7.30945987e+00 9.74466150e+00 3 -4.70973878e+00 4.92720508e+00 4.82400684e+00 | -4.70973878e+00 4.92720508e+00 4.82400684e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Fe, PBC = FFT (Configuration in file "config-AlFe-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.88073743021 2^p V(r_1,...,r_N) = -6.88073743021 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.29008218e+00 -1.04906992e+00 -8.92489096e-01 | -1.29008218e+00 -1.04906992e+00 -8.92489096e-01 1 4.56092983e+00 2.67620097e+00 -5.36990922e+00 | 4.56092983e+00 2.67620097e+00 -5.36990922e+00 2 1.39277632e+00 -2.43918292e+00 2.72534183e+00 | 1.39277632e+00 -2.43918292e+00 2.72534183e+00 3 -4.66362397e+00 8.12051872e-01 3.53705649e+00 | -4.66362397e+00 8.12051872e-01 3.53705649e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.