!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_MendelevAstaRahman_2009_AlMg__MO_658278549784_005 Supported species : Al Mg 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)) = -5.87663939662 2^p V(r_1,...,r_N) = -5.87663939662 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 -3.76270567e+00 -8.43365583e+00 -9.11935943e+00 | -3.76270567e+00 -8.43365583e+00 -9.11935943e+00 1 2.18731045e+00 1.48695106e+00 -1.01630469e+00 | 2.18731045e+00 1.48695106e+00 -1.01630469e+00 2 3.33995693e+00 -1.98704269e+00 3.33304158e+00 | 3.33995693e+00 -1.98704269e+00 3.33304158e+00 3 -1.76456171e+00 8.93374746e+00 6.80262253e+00 | -1.76456171e+00 8.93374746e+00 6.80262253e+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)) = -4.4644627226 2^p V(r_1,...,r_N) = -4.4644627226 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 -6.08319879e+00 -3.80113008e+00 -3.77893572e+00 | -6.08319879e+00 -3.80113008e+00 -3.77893572e+00 1 4.04301130e+00 3.68809190e+00 -5.16114776e+00 | 4.04301130e+00 3.68809190e+00 -5.16114776e+00 2 9.33171210e+00 -1.03323422e+01 7.16927773e+00 | 9.33171210e+00 -1.03323422e+01 7.16927773e+00 3 -7.29152461e+00 1.04453804e+01 1.77080574e+00 | -7.29152461e+00 1.04453804e+01 1.77080574e+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)) = -2.59919112506 2^p V(r_1,...,r_N) = -2.59919112506 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 -6.86473097e+00 -1.00045995e+01 -1.23405237e+01 | -6.86473097e+00 -1.00045995e+01 -1.23405237e+01 1 9.16877974e+00 9.52843913e+00 -5.22515775e+00 | 9.16877974e+00 9.52843913e+00 -5.22515775e+00 2 5.39074405e+00 -7.60203475e+00 8.40041849e+00 | 5.39074405e+00 -7.60203475e+00 8.40041849e+00 3 -7.69479282e+00 8.07819515e+00 9.16526293e+00 | -7.69479282e+00 8.07819515e+00 9.16526293e+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)) = 6.19877277453 2^p V(r_1,...,r_N) = 6.19877277453 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 -1.75258969e+01 -1.52058861e+01 -2.94229440e+01 | -1.75258969e+01 -1.52058861e+01 -2.94229440e+01 1 7.57978221e+00 9.99382903e+00 -6.16681062e+00 | 7.57978221e+00 9.99382903e+00 -6.16681062e+00 2 2.19317287e+01 -1.16894962e+01 2.20609449e+01 | 2.19317287e+01 -1.16894962e+01 2.20609449e+01 3 -1.19856141e+01 1.69015532e+01 1.35288097e+01 | -1.19856141e+01 1.69015532e+01 1.35288097e+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)) = -2.92299188065 2^p V(r_1,...,r_N) = -2.92299188065 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 -9.69034407e+00 -6.70134669e+00 -9.59237182e+00 | -9.69034407e+00 -6.70134669e+00 -9.59237182e+00 1 5.80727132e+00 8.51738220e+00 -6.87879389e+00 | 5.80727132e+00 8.51738220e+00 -6.87879389e+00 2 9.38088276e+00 -9.88280803e+00 8.96922561e+00 | 9.38088276e+00 -9.88280803e+00 8.96922561e+00 3 -5.49781001e+00 8.06677252e+00 7.50194010e+00 | -5.49781001e+00 8.06677252e+00 7.50194010e+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)) = -6.05523680189 2^p V(r_1,...,r_N) = -6.05523680189 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 -7.54283452e+00 -5.74710276e+00 -3.83279054e+00 | -7.54283452e+00 -5.74710276e+00 -3.83279054e+00 1 4.50910246e+00 6.05402759e+00 -4.77549108e+00 | 4.50910246e+00 6.05402759e+00 -4.77549108e+00 2 4.66800864e+00 -2.40731958e+00 7.32259522e+00 | 4.66800864e+00 -2.40731958e+00 7.32259522e+00 3 -1.63427658e+00 2.10039474e+00 1.28568640e+00 | -1.63427658e+00 2.10039474e+00 1.28568640e+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)) = 4.2126165164 2^p V(r_1,...,r_N) = 4.2126165164 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 -8.05397942e+00 -7.15362088e+00 -9.17752285e+00 | -8.05397942e+00 -7.15362088e+00 -9.17752285e+00 1 1.02299114e+01 1.07136856e+01 -8.58838177e+00 | 1.02299114e+01 1.07136856e+01 -8.58838177e+00 2 2.07640098e+01 -2.40905007e+01 1.18696797e+01 | 2.07640098e+01 -2.40905007e+01 1.18696797e+01 3 -2.29399418e+01 2.05304361e+01 5.89622496e+00 | -2.29399418e+01 2.05304361e+01 5.89622496e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TTT (Configuration in file "config-Mg-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)) = 4.15440508 2^p V(r_1,...,r_N) = 4.15440508 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 -4.94799994e+00 -3.13139949e+00 -5.66872363e+00 | -4.94799994e+00 -3.13139949e+00 -5.66872363e+00 1 3.45558781e+00 4.06726397e+00 -3.62572969e+00 | 3.45558781e+00 4.06726397e+00 -3.62572969e+00 2 6.17208462e+00 -4.92249289e+00 5.55736255e+00 | 6.17208462e+00 -4.92249289e+00 5.55736255e+00 3 -4.67967249e+00 3.98662841e+00 3.73709077e+00 | -4.67967249e+00 3.98662841e+00 3.73709077e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TTF (Configuration in file "config-Mg-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)) = 4.70432990841 2^p V(r_1,...,r_N) = 4.70432990841 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 -4.03440532e+00 -3.59098793e+00 -4.11971088e+00 | -4.03440532e+00 -3.59098793e+00 -4.11971088e+00 1 3.75436624e+00 4.51074853e+00 -4.40274038e+00 | 3.75436624e+00 4.51074853e+00 -4.40274038e+00 2 7.83807904e+00 -7.09045760e+00 4.53950188e+00 | 7.83807904e+00 -7.09045760e+00 4.53950188e+00 3 -7.55803996e+00 6.17069700e+00 3.98294938e+00 | -7.55803996e+00 6.17069700e+00 3.98294938e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TFT (Configuration in file "config-Mg-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)) = 2.12631439097 2^p V(r_1,...,r_N) = 2.12631439097 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 -2.76461869e+00 -2.48982581e+00 -2.28805098e+00 | -2.76461869e+00 -2.48982581e+00 -2.28805098e+00 1 3.17312105e+00 2.80099204e+00 -4.96332925e+00 | 3.17312105e+00 2.80099204e+00 -4.96332925e+00 2 2.74691912e+00 -3.83964997e+00 5.07439840e+00 | 2.74691912e+00 -3.83964997e+00 5.07439840e+00 3 -3.15542148e+00 3.52848374e+00 2.17698184e+00 | -3.15542148e+00 3.52848374e+00 2.17698184e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = TFF (Configuration in file "config-Mg-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)) = 2.43813203248 2^p V(r_1,...,r_N) = 2.43813203248 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 -3.33922133e+00 -5.93558631e+00 -5.03200761e+00 | -3.33922133e+00 -5.93558631e+00 -5.03200761e+00 1 2.93833188e+00 2.59377618e+00 -2.93590288e+00 | 2.93833188e+00 2.59377618e+00 -2.93590288e+00 2 2.61449139e+00 -2.79518574e+00 2.57472273e+00 | 2.61449139e+00 -2.79518574e+00 2.57472273e+00 3 -2.21360193e+00 6.13699587e+00 5.39318776e+00 | -2.21360193e+00 6.13699587e+00 5.39318776e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = FTT (Configuration in file "config-Mg-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)) = 0.280848116672 2^p V(r_1,...,r_N) = 0.280848116672 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 -2.26734832e+00 -2.16653599e+00 -2.35376178e+00 | -2.26734832e+00 -2.16653599e+00 -2.35376178e+00 1 2.98132924e+00 2.45318719e+00 -2.27325688e+00 | 2.98132924e+00 2.45318719e+00 -2.27325688e+00 2 1.77547239e+00 -2.44340467e+00 2.25749728e+00 | 1.77547239e+00 -2.44340467e+00 2.25749728e+00 3 -2.48945330e+00 2.15675348e+00 2.36952138e+00 | -2.48945330e+00 2.15675348e+00 2.36952138e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = FTF (Configuration in file "config-Mg-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)) = 1.58342315886 2^p V(r_1,...,r_N) = 1.58342315886 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 -2.39119911e+00 -4.28487739e+00 -3.83767453e+00 | -2.39119911e+00 -4.28487739e+00 -3.83767453e+00 1 2.27627656e+00 2.86214791e+00 -2.66147016e+00 | 2.27627656e+00 2.86214791e+00 -2.66147016e+00 2 2.94380346e+00 -2.12370597e+00 1.97739161e+00 | 2.94380346e+00 -2.12370597e+00 1.97739161e+00 3 -2.82888091e+00 3.54643545e+00 4.52175308e+00 | -2.82888091e+00 3.54643545e+00 4.52175308e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Mg, PBC = FFT (Configuration in file "config-Mg-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)) = 7.02346594666 2^p V(r_1,...,r_N) = 7.02346594666 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 -6.57103893e+00 -4.94691323e+00 -5.80581559e+00 | -6.57103893e+00 -4.94691323e+00 -5.80581559e+00 1 5.37721421e+00 4.06006644e+00 -6.47919477e+00 | 5.37721421e+00 4.06006644e+00 -6.47919477e+00 2 8.23358190e+00 -9.91843125e+00 8.99151632e+00 | 8.23358190e+00 -9.91843125e+00 8.99151632e+00 3 -7.03975718e+00 1.08052780e+01 3.29349404e+00 | -7.03975718e+00 1.08052780e+01 3.29349404e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = TTT (Configuration in file "config-AlMg-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)) = 2.39402423536 2^p V(r_1,...,r_N) = 2.39402423536 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 -4.20206318e+00 -3.26366507e+00 -3.02573553e+00 | -4.20206318e+00 -3.26366507e+00 -3.02573553e+00 1 6.47981488e+00 6.28866913e+00 -9.52528424e+00 | 6.47981488e+00 6.28866913e+00 -9.52528424e+00 2 8.64667259e+00 -1.08762121e+01 7.60888484e+00 | 8.64667259e+00 -1.08762121e+01 7.60888484e+00 3 -1.09244243e+01 7.85120803e+00 4.94213493e+00 | -1.09244243e+01 7.85120803e+00 4.94213493e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = TTF (Configuration in file "config-AlMg-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)) = 1.36715935134 2^p V(r_1,...,r_N) = 1.36715935134 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 -8.00990756e+00 -3.98162708e+00 -5.83726569e+00 | -8.00990756e+00 -3.98162708e+00 -5.83726569e+00 1 7.04948245e+00 9.07103001e+00 -6.53544185e+00 | 7.04948245e+00 9.07103001e+00 -6.53544185e+00 2 5.76415639e+00 -9.52446814e+00 8.20614465e+00 | 5.76415639e+00 -9.52446814e+00 8.20614465e+00 3 -4.80373127e+00 4.43506521e+00 4.16656289e+00 | -4.80373127e+00 4.43506521e+00 4.16656289e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = TFT (Configuration in file "config-AlMg-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)) = 0.321213943427 2^p V(r_1,...,r_N) = 0.321213943427 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 -5.93713710e+00 -4.29887889e+00 -5.98950840e+00 | -5.93713710e+00 -4.29887889e+00 -5.98950840e+00 1 5.42687217e+00 3.46747541e+00 -3.16927727e+00 | 5.42687217e+00 3.46747541e+00 -3.16927727e+00 2 6.59337429e+00 -6.11368700e+00 4.99317846e+00 | 6.59337429e+00 -6.11368700e+00 4.99317846e+00 3 -6.08310936e+00 6.94509048e+00 4.16560721e+00 | -6.08310936e+00 6.94509048e+00 4.16560721e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = TFF (Configuration in file "config-AlMg-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)) = -4.03948996393 2^p V(r_1,...,r_N) = -4.03948996393 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 -2.45754195e+00 -2.28357901e+00 -2.33258706e+00 | -2.45754195e+00 -2.28357901e+00 -2.33258706e+00 1 2.13512619e+00 2.87571730e+00 -1.87530884e+00 | 2.13512619e+00 2.87571730e+00 -1.87530884e+00 2 2.48098515e+00 -2.58858234e+00 1.94851065e+00 | 2.48098515e+00 -2.58858234e+00 1.94851065e+00 3 -2.15856940e+00 1.99644405e+00 2.25938526e+00 | -2.15856940e+00 1.99644405e+00 2.25938526e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = FTT (Configuration in file "config-AlMg-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)) = -4.3447659122 2^p V(r_1,...,r_N) = -4.3447659122 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 -2.49104010e+00 -2.21194851e+00 -1.55482586e+00 | -2.49104010e+00 -2.21194851e+00 -1.55482586e+00 1 2.56315364e+00 1.37474585e+00 -5.73648331e-01 | 2.56315364e+00 1.37474585e+00 -5.73648331e-01 2 2.09531490e+00 -1.93912131e+00 4.58435820e-01 | 2.09531490e+00 -1.93912131e+00 4.58435820e-01 3 -2.16742844e+00 2.77632396e+00 1.67003837e+00 | -2.16742844e+00 2.77632396e+00 1.67003837e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = FTF (Configuration in file "config-AlMg-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)) = -0.503809497335 2^p V(r_1,...,r_N) = -0.503809497335 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 -6.44633544e+00 -5.99340727e+00 -1.03860342e+01 | -6.44633544e+00 -5.99340727e+00 -1.03860342e+01 1 2.25175271e+00 2.88412257e+00 -2.41859695e+00 | 2.25175271e+00 2.88412257e+00 -2.41859695e+00 2 9.09127344e+00 -2.33797053e+00 1.03541434e+01 | 9.09127344e+00 -2.33797053e+00 1.03541434e+01 3 -4.89669071e+00 5.44725524e+00 2.45048783e+00 | -4.89669071e+00 5.44725524e+00 2.45048783e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Mg, PBC = FFT (Configuration in file "config-AlMg-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)) = -0.526186421911 2^p V(r_1,...,r_N) = -0.526186421911 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 -5.30171533e+00 -5.08999058e+00 -3.13100173e+00 | -5.30171533e+00 -5.08999058e+00 -3.13100173e+00 1 4.08763162e+00 7.43835788e+00 -7.63766958e+00 | 4.08763162e+00 7.43835788e+00 -7.63766958e+00 2 5.15265415e+00 -4.55223104e+00 5.17183301e+00 | 5.15265415e+00 -4.55223104e+00 5.17183301e+00 3 -3.93857044e+00 2.20386374e+00 5.59683830e+00 | -3.93857044e+00 2.20386374e+00 5.59683830e+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.