!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_ZhouZimmermanWong_2008_PdH__MO_114797992931_000 Supported species : H Pd random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TTT (Configuration in file "config-H-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)) = -0.527728198199 2^p V(r_1,...,r_N) = -0.527728198199 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 -7.91003987e-01 -2.30305358e+00 -2.44783493e+00 | -7.91003987e-01 -2.30305358e+00 -2.44783493e+00 1 5.61317117e-01 4.97080868e-01 -3.89016179e-01 | 5.61317117e-01 4.97080868e-01 -3.89016179e-01 2 6.25255435e-01 -5.54778883e-01 9.11402903e-01 | 6.25255435e-01 -5.54778883e-01 9.11402903e-01 3 -3.95568564e-01 2.36075160e+00 1.92544820e+00 | -3.95568564e-01 2.36075160e+00 1.92544820e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TTF (Configuration in file "config-H-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)) = 1.81927882733 2^p V(r_1,...,r_N) = 1.81927882733 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 -7.39413310e-01 -1.11177690e+00 -7.59721726e-01 | -7.39413310e-01 -1.11177690e+00 -7.59721726e-01 1 7.28651637e+00 2.26926484e+00 -8.61201046e+00 | 7.28651637e+00 2.26926484e+00 -8.61201046e+00 2 1.95443429e+00 -2.15808789e+00 1.36960918e+00 | 1.95443429e+00 -2.15808789e+00 1.36960918e+00 3 -8.50153734e+00 1.00059995e+00 8.00212301e+00 | -8.50153734e+00 1.00059995e+00 8.00212301e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TFT (Configuration in file "config-H-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)) = 0.835258061218 2^p V(r_1,...,r_N) = 0.835258061218 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 -1.32470865e+00 -6.00316012e+00 -6.23511953e+00 | -1.32470865e+00 -6.00316012e+00 -6.23511953e+00 1 8.26272417e-01 4.51228713e-01 -7.38805244e-01 | 8.26272417e-01 4.51228713e-01 -7.38805244e-01 2 5.80279659e-01 -6.49626994e-01 3.99291802e-01 | 5.80279659e-01 -6.49626994e-01 3.99291802e-01 3 -8.18434285e-02 6.20155840e+00 6.57463298e+00 | -8.18434285e-02 6.20155840e+00 6.57463298e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TFF (Configuration in file "config-H-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)) = 0.42616124575 2^p V(r_1,...,r_N) = 0.42616124575 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 -2.07003648e+00 -1.85796702e+00 -1.45896745e+00 | -2.07003648e+00 -1.85796702e+00 -1.45896745e+00 1 3.39917868e+00 3.15252973e+00 -2.74362199e+00 | 3.39917868e+00 3.15252973e+00 -2.74362199e+00 2 1.83259699e+00 -2.62403664e+00 1.05044345e+00 | 1.83259699e+00 -2.62403664e+00 1.05044345e+00 3 -3.16173920e+00 1.32947393e+00 3.15214599e+00 | -3.16173920e+00 1.32947393e+00 3.15214599e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = FTT (Configuration in file "config-H-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)) = 0.882249547817 2^p V(r_1,...,r_N) = 0.882249547817 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 -2.16291707e+00 -5.46933057e+00 -3.69090151e+00 | -2.16291707e+00 -5.46933057e+00 -3.69090151e+00 1 3.59703804e+00 3.18072819e+00 -1.99798770e+00 | 3.59703804e+00 3.18072819e+00 -1.99798770e+00 2 1.63805294e+00 -6.85173575e-01 1.70507912e+00 | 1.63805294e+00 -6.85173575e-01 1.70507912e+00 3 -3.07217391e+00 2.97377595e+00 3.98381009e+00 | -3.07217391e+00 2.97377595e+00 3.98381009e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = FTF (Configuration in file "config-H-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)) = -0.777589052743 2^p V(r_1,...,r_N) = -0.777589052743 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 -4.40465673e-01 -1.75876976e-01 -3.41504376e-01 | -4.40465673e-01 -1.75876976e-01 -3.41504376e-01 1 2.34141739e-01 8.54707709e-01 -5.99983346e-01 | 2.34141739e-01 8.54707709e-01 -5.99983346e-01 2 1.59657288e+00 -1.81815597e+00 5.54566626e-01 | 1.59657288e+00 -1.81815597e+00 5.54566626e-01 3 -1.39024895e+00 1.13932523e+00 3.86921096e-01 | -1.39024895e+00 1.13932523e+00 3.86921096e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = FFT (Configuration in file "config-H-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)) = 1.66376789175 2^p V(r_1,...,r_N) = 1.66376789175 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 -1.96211619e+00 -5.01353733e+00 -2.38495403e+00 | -1.96211619e+00 -5.01353733e+00 -2.38495403e+00 1 6.07049515e+00 2.24843001e+00 -6.27282978e+00 | 6.07049515e+00 2.24843001e+00 -6.27282978e+00 2 9.75037710e-01 -8.40192908e-01 8.74643503e-01 | 9.75037710e-01 -8.40192908e-01 8.74643503e-01 3 -5.08341667e+00 3.60530023e+00 7.78314031e+00 | -5.08341667e+00 3.60530023e+00 7.78314031e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TTT (Configuration in file "config-Pd-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)) = 2.23117640323 2^p V(r_1,...,r_N) = 2.23117640323 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 -4.50866770e+00 -5.57963726e+00 -6.30585854e+00 | -4.50866770e+00 -5.57963726e+00 -6.30585854e+00 1 5.11323818e+00 4.81468346e+00 -3.44233105e+00 | 5.11323818e+00 4.81468346e+00 -3.44233105e+00 2 4.63705813e+00 -4.12732622e+00 4.11929139e+00 | 4.63705813e+00 -4.12732622e+00 4.11929139e+00 3 -5.24162861e+00 4.89228002e+00 5.62889821e+00 | -5.24162861e+00 4.89228002e+00 5.62889821e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TTF (Configuration in file "config-Pd-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)) = 0.371989138333 2^p V(r_1,...,r_N) = 0.371989138333 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 -1.56689152e+00 -1.04567075e+00 -1.77499492e+00 | -1.56689152e+00 -1.04567075e+00 -1.77499492e+00 1 2.04532366e+00 2.27281862e+00 -3.49405897e+00 | 2.04532366e+00 2.27281862e+00 -3.49405897e+00 2 3.47677498e+00 -3.81018595e+00 2.90663099e+00 | 3.47677498e+00 -3.81018595e+00 2.90663099e+00 3 -3.95520712e+00 2.58303808e+00 2.36242290e+00 | -3.95520712e+00 2.58303808e+00 2.36242290e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TFT (Configuration in file "config-Pd-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)) = -0.834891023989 2^p V(r_1,...,r_N) = -0.834891023989 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 -4.95231090e-01 -5.21864657e-01 -9.82010725e-01 | -4.95231090e-01 -5.21864657e-01 -9.82010725e-01 1 6.21797506e-01 1.34120905e+00 -1.11926277e+00 | 6.21797506e-01 1.34120905e+00 -1.11926277e+00 2 6.29439307e-01 -1.75805845e+00 1.51890519e+00 | 6.29439307e-01 -1.75805845e+00 1.51890519e+00 3 -7.56005722e-01 9.38714059e-01 5.82368307e-01 | -7.56005722e-01 9.38714059e-01 5.82368307e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TFF (Configuration in file "config-Pd-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)) = 2.06495835159 2^p V(r_1,...,r_N) = 2.06495835159 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 -3.01223518e+00 -5.80017970e+00 -3.04273626e+00 | -3.01223518e+00 -5.80017970e+00 -3.04273626e+00 1 4.10684366e+00 2.44957427e+00 -3.12046353e+00 | 4.10684366e+00 2.44957427e+00 -3.12046353e+00 2 1.53120301e+00 -7.50845332e-01 7.56813134e-01 | 1.53120301e+00 -7.50845332e-01 7.56813134e-01 3 -2.62581149e+00 4.10145076e+00 5.40638666e+00 | -2.62581149e+00 4.10145076e+00 5.40638666e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = FTT (Configuration in file "config-Pd-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)) = -0.866826677328 2^p V(r_1,...,r_N) = -0.866826677328 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 -1.26258123e+00 -1.47913072e+00 -9.87505564e-01 | -1.26258123e+00 -1.47913072e+00 -9.87505564e-01 1 1.38946868e+00 1.05042127e+00 -1.07920101e+00 | 1.38946868e+00 1.05042127e+00 -1.07920101e+00 2 3.70254953e-01 -5.97682240e-01 5.27299740e-01 | 3.70254953e-01 -5.97682240e-01 5.27299740e-01 3 -4.97142398e-01 1.02639169e+00 1.53940683e+00 | -4.97142398e-01 1.02639169e+00 1.53940683e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = FTF (Configuration in file "config-Pd-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)) = 0.112963873668 2^p V(r_1,...,r_N) = 0.112963873668 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 -3.20108004e+00 -1.45787029e+00 -4.05216011e+00 | -3.20108004e+00 -1.45787029e+00 -4.05216011e+00 1 1.18822958e+00 1.18788591e+00 -6.35218419e-01 | 1.18822958e+00 1.18788591e+00 -6.35218419e-01 2 3.42607543e+00 -2.54666638e+00 1.77650045e+00 | 3.42607543e+00 -2.54666638e+00 1.77650045e+00 3 -1.41322497e+00 2.81665077e+00 2.91087808e+00 | -1.41322497e+00 2.81665077e+00 2.91087808e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = FFT (Configuration in file "config-Pd-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)) = -0.349881236786 2^p V(r_1,...,r_N) = -0.349881236786 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 -2.51511737e+00 -2.71153453e+00 -2.26865973e+00 | -2.51511737e+00 -2.71153453e+00 -2.26865973e+00 1 2.14198888e+00 2.41842913e+00 -4.03227872e-01 | 2.14198888e+00 2.41842913e+00 -4.03227872e-01 2 8.76731845e-01 -5.60615698e-01 1.19141076e+00 | 8.76731845e-01 -5.60615698e-01 1.19141076e+00 3 -5.03603357e-01 8.53721095e-01 1.48047684e+00 | -5.03603357e-01 8.53721095e-01 1.48047684e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Pd, PBC = TTT (Configuration in file "config-HPd-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)) = -1.35721341832 2^p V(r_1,...,r_N) = -1.35721341832 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 2.03018269e-01 5.41131010e-01 1.51371303e-01 | 2.03018269e-01 5.41131010e-01 1.51371303e-01 1 8.14009976e-01 -7.80432477e-01 -7.69147511e-01 | 8.14009976e-01 -7.80432477e-01 -7.69147511e-01 2 -8.28364430e-01 1.46465023e+00 -4.92475972e-01 | -8.28364430e-01 1.46465023e+00 -4.92475972e-01 3 -1.88663815e-01 -1.22534877e+00 1.11025218e+00 | -1.88663815e-01 -1.22534877e+00 1.11025218e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Pd, PBC = TTF (Configuration in file "config-HPd-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)) = -1.56506511857 2^p V(r_1,...,r_N) = -1.56506511857 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 1.80916045e-01 1.24759679e+00 1.60681690e-01 | 1.80916045e-01 1.24759679e+00 1.60681690e-01 1 -4.72516084e-01 -1.20927759e+00 5.26001026e-01 | -4.72516084e-01 -1.20927759e+00 5.26001026e-01 2 -1.33684181e-01 1.03338245e+00 4.27611139e-02 | -1.33684181e-01 1.03338245e+00 4.27611139e-02 3 4.25284219e-01 -1.07170165e+00 -7.29443829e-01 | 4.25284219e-01 -1.07170165e+00 -7.29443829e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Pd, PBC = TFT (Configuration in file "config-HPd-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)) = -1.85838852256 2^p V(r_1,...,r_N) = -1.85838852256 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 3.25959541e-02 -1.77946898e-02 1.39456548e+00 | 3.25959541e-02 -1.77946898e-02 1.39456548e+00 1 -6.82587940e-01 -4.47544507e-01 1.85991798e+00 | -6.82587940e-01 -4.47544507e-01 1.85991798e+00 2 9.02322764e-01 -7.78637563e-01 -1.50878404e+00 | 9.02322764e-01 -7.78637563e-01 -1.50878404e+00 3 -2.52330778e-01 1.24397676e+00 -1.74569942e+00 | -2.52330778e-01 1.24397676e+00 -1.74569942e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Pd, PBC = TFF (Configuration in file "config-HPd-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)) = -1.63064307471 2^p V(r_1,...,r_N) = -1.63064307471 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 6.28344098e-01 3.11760207e-01 4.11045879e-01 | 6.28344098e-01 3.11760207e-01 4.11045879e-01 1 -1.15205688e+00 -6.31106206e-03 5.81471357e-01 | -1.15205688e+00 -6.31106206e-03 5.81471357e-01 2 -6.90366910e-01 3.09241337e-01 -1.04801700e-01 | -6.90366910e-01 3.09241337e-01 -1.04801700e-01 3 1.21407969e+00 -6.14690482e-01 -8.87715537e-01 | 1.21407969e+00 -6.14690482e-01 -8.87715537e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Pd, PBC = FTT (Configuration in file "config-HPd-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)) = -1.36935664116 2^p V(r_1,...,r_N) = -1.36935664116 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 4.02125912e-01 1.47083953e+00 3.50751398e-01 | 4.02125912e-01 1.47083953e+00 3.50751398e-01 1 1.57877127e-01 -1.41236302e+00 -2.32104463e-01 | 1.57877127e-01 -1.41236302e+00 -2.32104463e-01 2 -3.04693633e-01 1.30670883e+00 -3.21139351e-01 | -3.04693633e-01 1.30670883e+00 -3.21139351e-01 3 -2.55309407e-01 -1.36518534e+00 2.02492415e-01 | -2.55309407e-01 -1.36518534e+00 2.02492415e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Pd, PBC = FTF (Configuration in file "config-HPd-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)) = -2.79160639519 2^p V(r_1,...,r_N) = -2.79160639519 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 -1.33214502e+00 1.48914616e+00 -2.71664393e-01 | -1.33214502e+00 1.48914616e+00 -2.71664393e-01 1 -7.91186944e-01 -1.42903025e+00 9.94456908e-01 | -7.91186944e-01 -1.42903025e+00 9.94456908e-01 2 1.11101907e+00 1.57002887e+00 4.06339233e-01 | 1.11101907e+00 1.57002887e+00 4.06339233e-01 3 1.01231289e+00 -1.63014478e+00 -1.12913175e+00 | 1.01231289e+00 -1.63014478e+00 -1.12913175e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H Pd, PBC = FFT (Configuration in file "config-HPd-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)) = -2.38275798209 2^p V(r_1,...,r_N) = -2.38275798209 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 -8.74241474e-01 -6.21548417e-01 2.59912033e+00 | -8.74241474e-01 -6.21548417e-01 2.59912033e+00 1 1.53072382e+00 9.48624816e-01 1.13702001e+00 | 1.53072382e+00 9.48624816e-01 1.13702001e+00 2 -2.96559957e-01 -5.35794555e-02 -2.37792866e+00 | -2.96559957e-01 -5.35794555e-02 -2.37792866e+00 3 -3.59922386e-01 -2.73496943e-01 -1.35821168e+00 | -3.59922386e-01 -2.73496943e-01 -1.35821168e+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.