!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_BonnyGrigorevTerentyev_2014EAM1_WHHe__MO_292520929154_000 Supported species : H He W 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=3 periodic directions, which means an increase by a factor n=2^3=8 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)) = 14.83054011166633 2^p V(r_1,...,r_N) = 14.83054011166635 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 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 | 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 1 -6.74558618e-01 3.32400567e-01 -2.78839483e-01 | -6.74558618e-01 3.32400567e-01 -2.78839483e-01 2 -1.22425994e-01 -6.56411217e-02 2.95327484e-02 | -1.22425994e-01 -6.56411217e-02 2.95327484e-02 3 3.95539696e-01 1.37432927e-01 4.27505312e-01 | 3.95539696e-01 1.37432927e-01 4.27505312e-01 4 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 | 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 5 -6.74558618e-01 3.32400567e-01 -2.78839483e-01 | -6.74558618e-01 3.32400567e-01 -2.78839483e-01 6 -1.22425994e-01 -6.56411217e-02 2.95327484e-02 | -1.22425994e-01 -6.56411217e-02 2.95327484e-02 7 3.95539696e-01 1.37432927e-01 4.27505312e-01 | 3.95539696e-01 1.37432927e-01 4.27505312e-01 8 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 | 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 9 -6.74558618e-01 3.32400567e-01 -2.78839483e-01 | -6.74558618e-01 3.32400567e-01 -2.78839483e-01 10 -1.22425994e-01 -6.56411217e-02 2.95327484e-02 | -1.22425994e-01 -6.56411217e-02 2.95327484e-02 11 3.95539696e-01 1.37432927e-01 4.27505312e-01 | 3.95539696e-01 1.37432927e-01 4.27505312e-01 12 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 | 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 13 -6.74558618e-01 3.32400567e-01 -2.78839483e-01 | -6.74558618e-01 3.32400567e-01 -2.78839483e-01 14 -1.22425994e-01 -6.56411217e-02 2.95327484e-02 | -1.22425994e-01 -6.56411217e-02 2.95327484e-02 15 3.95539696e-01 1.37432927e-01 4.27505312e-01 | 3.95539696e-01 1.37432927e-01 4.27505312e-01 16 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 | 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 17 -6.74558618e-01 3.32400567e-01 -2.78839483e-01 | -6.74558618e-01 3.32400567e-01 -2.78839483e-01 18 -1.22425994e-01 -6.56411217e-02 2.95327484e-02 | -1.22425994e-01 -6.56411217e-02 2.95327484e-02 19 3.95539696e-01 1.37432927e-01 4.27505312e-01 | 3.95539696e-01 1.37432927e-01 4.27505312e-01 20 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 | 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 21 -6.74558618e-01 3.32400567e-01 -2.78839483e-01 | -6.74558618e-01 3.32400567e-01 -2.78839483e-01 22 -1.22425994e-01 -6.56411217e-02 2.95327484e-02 | -1.22425994e-01 -6.56411217e-02 2.95327484e-02 23 3.95539696e-01 1.37432927e-01 4.27505312e-01 | 3.95539696e-01 1.37432927e-01 4.27505312e-01 24 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 | 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 25 -6.74558618e-01 3.32400567e-01 -2.78839483e-01 | -6.74558618e-01 3.32400567e-01 -2.78839483e-01 26 -1.22425994e-01 -6.56411217e-02 2.95327484e-02 | -1.22425994e-01 -6.56411217e-02 2.95327484e-02 27 3.95539696e-01 1.37432927e-01 4.27505312e-01 | 3.95539696e-01 1.37432927e-01 4.27505312e-01 28 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 | 4.01444915e-01 -4.04192373e-01 -1.78198577e-01 29 -6.74558618e-01 3.32400567e-01 -2.78839483e-01 | -6.74558618e-01 3.32400567e-01 -2.78839483e-01 30 -1.22425994e-01 -6.56411217e-02 2.95327484e-02 | -1.22425994e-01 -6.56411217e-02 2.95327484e-02 31 3.95539696e-01 1.37432927e-01 4.27505312e-01 | 3.95539696e-01 1.37432927e-01 4.27505312e-01 ------------------------------------------------------------------------------------------------------------------------ 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=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 6.483693846033339 2^p V(r_1,...,r_N) = 6.483693846033336 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 6.70206125e-01 6.50393100e-01 -8.83830173e-01 | 6.70206125e-01 6.50393100e-01 -8.83830173e-01 1 -8.04130579e-01 -4.27320874e-01 -9.13410441e-01 | -8.04130579e-01 -4.27320874e-01 -9.13410441e-01 2 -4.65165726e-01 -2.08569576e-01 8.18070184e-01 | -4.65165726e-01 -2.08569576e-01 8.18070184e-01 3 5.99090180e-01 -1.45026504e-02 9.79170429e-01 | 5.99090180e-01 -1.45026504e-02 9.79170429e-01 4 6.70206125e-01 6.50393100e-01 -8.83830173e-01 | 6.70206125e-01 6.50393100e-01 -8.83830173e-01 5 -8.04130579e-01 -4.27320874e-01 -9.13410441e-01 | -8.04130579e-01 -4.27320874e-01 -9.13410441e-01 6 -4.65165726e-01 -2.08569576e-01 8.18070184e-01 | -4.65165726e-01 -2.08569576e-01 8.18070184e-01 7 5.99090180e-01 -1.45026504e-02 9.79170429e-01 | 5.99090180e-01 -1.45026504e-02 9.79170429e-01 8 6.70206125e-01 6.50393100e-01 -8.83830173e-01 | 6.70206125e-01 6.50393100e-01 -8.83830173e-01 9 -8.04130579e-01 -4.27320874e-01 -9.13410441e-01 | -8.04130579e-01 -4.27320874e-01 -9.13410441e-01 10 -4.65165726e-01 -2.08569576e-01 8.18070184e-01 | -4.65165726e-01 -2.08569576e-01 8.18070184e-01 11 5.99090180e-01 -1.45026504e-02 9.79170429e-01 | 5.99090180e-01 -1.45026504e-02 9.79170429e-01 12 6.70206125e-01 6.50393100e-01 -8.83830173e-01 | 6.70206125e-01 6.50393100e-01 -8.83830173e-01 13 -8.04130579e-01 -4.27320874e-01 -9.13410441e-01 | -8.04130579e-01 -4.27320874e-01 -9.13410441e-01 14 -4.65165726e-01 -2.08569576e-01 8.18070184e-01 | -4.65165726e-01 -2.08569576e-01 8.18070184e-01 15 5.99090180e-01 -1.45026504e-02 9.79170429e-01 | 5.99090180e-01 -1.45026504e-02 9.79170429e-01 ------------------------------------------------------------------------------------------------------------------------ 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=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 6.233488531221699 2^p V(r_1,...,r_N) = 6.233488531221697 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 3.39499858e-01 -8.66555928e-01 -3.24245440e-01 | 3.39499858e-01 -8.66555928e-01 -3.24245440e-01 1 -4.80083548e-01 8.84789326e-01 -9.87013673e-02 | -4.80083548e-01 8.84789326e-01 -9.87013673e-02 2 -4.51117751e-01 -9.68791178e-01 1.92676866e-01 | -4.51117751e-01 -9.68791178e-01 1.92676866e-01 3 5.91701442e-01 9.50557779e-01 2.30269941e-01 | 5.91701442e-01 9.50557779e-01 2.30269941e-01 4 3.39499858e-01 -8.66555928e-01 -3.24245440e-01 | 3.39499858e-01 -8.66555928e-01 -3.24245440e-01 5 -4.80083548e-01 8.84789326e-01 -9.87013673e-02 | -4.80083548e-01 8.84789326e-01 -9.87013673e-02 6 -4.51117751e-01 -9.68791178e-01 1.92676866e-01 | -4.51117751e-01 -9.68791178e-01 1.92676866e-01 7 5.91701442e-01 9.50557779e-01 2.30269941e-01 | 5.91701442e-01 9.50557779e-01 2.30269941e-01 8 3.39499858e-01 -8.66555928e-01 -3.24245440e-01 | 3.39499858e-01 -8.66555928e-01 -3.24245440e-01 9 -4.80083548e-01 8.84789326e-01 -9.87013673e-02 | -4.80083548e-01 8.84789326e-01 -9.87013673e-02 10 -4.51117751e-01 -9.68791178e-01 1.92676866e-01 | -4.51117751e-01 -9.68791178e-01 1.92676866e-01 11 5.91701442e-01 9.50557779e-01 2.30269941e-01 | 5.91701442e-01 9.50557779e-01 2.30269941e-01 12 3.39499858e-01 -8.66555928e-01 -3.24245440e-01 | 3.39499858e-01 -8.66555928e-01 -3.24245440e-01 13 -4.80083548e-01 8.84789326e-01 -9.87013673e-02 | -4.80083548e-01 8.84789326e-01 -9.87013673e-02 14 -4.51117751e-01 -9.68791178e-01 1.92676866e-01 | -4.51117751e-01 -9.68791178e-01 1.92676866e-01 15 5.91701442e-01 9.50557779e-01 2.30269941e-01 | 5.91701442e-01 9.50557779e-01 2.30269941e-01 ------------------------------------------------------------------------------------------------------------------------ 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=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 2.2783435359409534 2^p V(r_1,...,r_N) = 2.278343535940954 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 3.31323180e-01 -8.42683863e-01 -6.68151827e-01 | 3.31323180e-01 -8.42683863e-01 -6.68151827e-01 1 -3.73921493e-01 7.57803963e-01 -6.54804445e-01 | -3.73921493e-01 7.57803963e-01 -6.54804445e-01 2 -3.28706896e-01 -6.85262973e-01 6.84973910e-01 | -3.28706896e-01 -6.85262973e-01 6.84973910e-01 3 3.71305208e-01 7.70142874e-01 6.37982362e-01 | 3.71305208e-01 7.70142874e-01 6.37982362e-01 4 3.31323180e-01 -8.42683863e-01 -6.68151827e-01 | 3.31323180e-01 -8.42683863e-01 -6.68151827e-01 5 -3.73921493e-01 7.57803963e-01 -6.54804445e-01 | -3.73921493e-01 7.57803963e-01 -6.54804445e-01 6 -3.28706896e-01 -6.85262973e-01 6.84973910e-01 | -3.28706896e-01 -6.85262973e-01 6.84973910e-01 7 3.71305208e-01 7.70142874e-01 6.37982362e-01 | 3.71305208e-01 7.70142874e-01 6.37982362e-01 ------------------------------------------------------------------------------------------------------------------------ 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=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 6.165164999229539 2^p V(r_1,...,r_N) = 6.165164999229528 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 -7.20928543e-01 -1.43914785e-01 -1.60246420e-01 | -7.20928543e-01 -1.43914785e-01 -1.60246420e-01 1 7.13816182e-01 -3.93839318e-01 2.97529275e-01 | 7.13816182e-01 -3.93839318e-01 2.97529275e-01 2 8.41035935e-01 5.18046984e-01 -4.38549666e-01 | 8.41035935e-01 5.18046984e-01 -4.38549666e-01 3 -8.33923573e-01 1.97071186e-02 3.01266811e-01 | -8.33923573e-01 1.97071186e-02 3.01266811e-01 4 -7.20928543e-01 -1.43914785e-01 -1.60246420e-01 | -7.20928543e-01 -1.43914785e-01 -1.60246420e-01 5 7.13816182e-01 -3.93839318e-01 2.97529275e-01 | 7.13816182e-01 -3.93839318e-01 2.97529275e-01 6 8.41035935e-01 5.18046984e-01 -4.38549666e-01 | 8.41035935e-01 5.18046984e-01 -4.38549666e-01 7 -8.33923573e-01 1.97071186e-02 3.01266811e-01 | -8.33923573e-01 1.97071186e-02 3.01266811e-01 8 -7.20928543e-01 -1.43914785e-01 -1.60246420e-01 | -7.20928543e-01 -1.43914785e-01 -1.60246420e-01 9 7.13816182e-01 -3.93839318e-01 2.97529275e-01 | 7.13816182e-01 -3.93839318e-01 2.97529275e-01 10 8.41035935e-01 5.18046984e-01 -4.38549666e-01 | 8.41035935e-01 5.18046984e-01 -4.38549666e-01 11 -8.33923573e-01 1.97071186e-02 3.01266811e-01 | -8.33923573e-01 1.97071186e-02 3.01266811e-01 12 -7.20928543e-01 -1.43914785e-01 -1.60246420e-01 | -7.20928543e-01 -1.43914785e-01 -1.60246420e-01 13 7.13816182e-01 -3.93839318e-01 2.97529275e-01 | 7.13816182e-01 -3.93839318e-01 2.97529275e-01 14 8.41035935e-01 5.18046984e-01 -4.38549666e-01 | 8.41035935e-01 5.18046984e-01 -4.38549666e-01 15 -8.33923573e-01 1.97071186e-02 3.01266811e-01 | -8.33923573e-01 1.97071186e-02 3.01266811e-01 ------------------------------------------------------------------------------------------------------------------------ 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=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 2.6569923707851975 2^p V(r_1,...,r_N) = 2.656992370785197 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 -9.65254904e-01 4.71476244e-02 -8.90972819e-01 | -9.65254904e-01 4.71476244e-02 -8.90972819e-01 1 6.89320216e-01 6.96798454e-02 -7.40250957e-01 | 6.89320216e-01 6.96798454e-02 -7.40250957e-01 2 9.88702494e-01 9.72397866e-02 8.73850029e-01 | 9.88702494e-01 9.72397866e-02 8.73850029e-01 3 -7.12767807e-01 -2.14067256e-01 7.57373747e-01 | -7.12767807e-01 -2.14067256e-01 7.57373747e-01 4 -9.65254904e-01 4.71476244e-02 -8.90972819e-01 | -9.65254904e-01 4.71476244e-02 -8.90972819e-01 5 6.89320216e-01 6.96798454e-02 -7.40250957e-01 | 6.89320216e-01 6.96798454e-02 -7.40250957e-01 6 9.88702494e-01 9.72397866e-02 8.73850029e-01 | 9.88702494e-01 9.72397866e-02 8.73850029e-01 7 -7.12767807e-01 -2.14067256e-01 7.57373747e-01 | -7.12767807e-01 -2.14067256e-01 7.57373747e-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=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 3.3475531382454258 2^p V(r_1,...,r_N) = 3.347553138245425 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 -9.01944314e-01 -8.78338949e-01 3.59886739e-01 | -9.01944314e-01 -8.78338949e-01 3.59886739e-01 1 9.55994794e-01 8.40596581e-01 -3.72150154e-01 | 9.55994794e-01 8.40596581e-01 -3.72150154e-01 2 1.17233085e+00 -9.45489269e-01 -1.25904273e-01 | 1.17233085e+00 -9.45489269e-01 -1.25904273e-01 3 -1.22638133e+00 9.83231637e-01 1.38167689e-01 | -1.22638133e+00 9.83231637e-01 1.38167689e-01 4 -9.01944314e-01 -8.78338949e-01 3.59886739e-01 | -9.01944314e-01 -8.78338949e-01 3.59886739e-01 5 9.55994794e-01 8.40596581e-01 -3.72150154e-01 | 9.55994794e-01 8.40596581e-01 -3.72150154e-01 6 1.17233085e+00 -9.45489269e-01 -1.25904273e-01 | 1.17233085e+00 -9.45489269e-01 -1.25904273e-01 7 -1.22638133e+00 9.83231637e-01 1.38167689e-01 | -1.22638133e+00 9.83231637e-01 1.38167689e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = TTT (Configuration in file "config-He-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 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)) = -32.25107163686454 2^p V(r_1,...,r_N) = -32.251071636864474 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 4.38351614e-01 1.47435348e-01 4.12346054e-01 | 4.38351614e-01 1.47435348e-01 4.12346054e-01 1 -2.80617962e-01 -3.92080711e-01 8.28941631e-01 | -2.80617962e-01 -3.92080711e-01 8.28941631e-01 2 -4.15950338e-01 4.18213422e-01 -8.84444580e-01 | -4.15950338e-01 4.18213422e-01 -8.84444580e-01 3 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 | 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 4 4.38351614e-01 1.47435348e-01 4.12346054e-01 | 4.38351614e-01 1.47435348e-01 4.12346054e-01 5 -2.80617962e-01 -3.92080711e-01 8.28941631e-01 | -2.80617962e-01 -3.92080711e-01 8.28941631e-01 6 -4.15950338e-01 4.18213422e-01 -8.84444580e-01 | -4.15950338e-01 4.18213422e-01 -8.84444580e-01 7 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 | 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 8 4.38351614e-01 1.47435348e-01 4.12346054e-01 | 4.38351614e-01 1.47435348e-01 4.12346054e-01 9 -2.80617962e-01 -3.92080711e-01 8.28941631e-01 | -2.80617962e-01 -3.92080711e-01 8.28941631e-01 10 -4.15950338e-01 4.18213422e-01 -8.84444580e-01 | -4.15950338e-01 4.18213422e-01 -8.84444580e-01 11 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 | 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 12 4.38351614e-01 1.47435348e-01 4.12346054e-01 | 4.38351614e-01 1.47435348e-01 4.12346054e-01 13 -2.80617962e-01 -3.92080711e-01 8.28941631e-01 | -2.80617962e-01 -3.92080711e-01 8.28941631e-01 14 -4.15950338e-01 4.18213422e-01 -8.84444580e-01 | -4.15950338e-01 4.18213422e-01 -8.84444580e-01 15 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 | 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 16 4.38351614e-01 1.47435348e-01 4.12346054e-01 | 4.38351614e-01 1.47435348e-01 4.12346054e-01 17 -2.80617962e-01 -3.92080711e-01 8.28941631e-01 | -2.80617962e-01 -3.92080711e-01 8.28941631e-01 18 -4.15950338e-01 4.18213422e-01 -8.84444580e-01 | -4.15950338e-01 4.18213422e-01 -8.84444580e-01 19 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 | 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 20 4.38351614e-01 1.47435348e-01 4.12346054e-01 | 4.38351614e-01 1.47435348e-01 4.12346054e-01 21 -2.80617962e-01 -3.92080711e-01 8.28941631e-01 | -2.80617962e-01 -3.92080711e-01 8.28941631e-01 22 -4.15950338e-01 4.18213422e-01 -8.84444580e-01 | -4.15950338e-01 4.18213422e-01 -8.84444580e-01 23 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 | 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 24 4.38351614e-01 1.47435348e-01 4.12346054e-01 | 4.38351614e-01 1.47435348e-01 4.12346054e-01 25 -2.80617962e-01 -3.92080711e-01 8.28941631e-01 | -2.80617962e-01 -3.92080711e-01 8.28941631e-01 26 -4.15950338e-01 4.18213422e-01 -8.84444580e-01 | -4.15950338e-01 4.18213422e-01 -8.84444580e-01 27 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 | 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 28 4.38351614e-01 1.47435348e-01 4.12346054e-01 | 4.38351614e-01 1.47435348e-01 4.12346054e-01 29 -2.80617962e-01 -3.92080711e-01 8.28941631e-01 | -2.80617962e-01 -3.92080711e-01 8.28941631e-01 30 -4.15950338e-01 4.18213422e-01 -8.84444580e-01 | -4.15950338e-01 4.18213422e-01 -8.84444580e-01 31 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 | 2.58216686e-01 -1.73568059e-01 -3.56843105e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = TTF (Configuration in file "config-He-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = -13.579170317558775 2^p V(r_1,...,r_N) = -13.579170317558765 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 5.78887034e-01 3.04035069e-02 1.49444455e+00 | 5.78887034e-01 3.04035069e-02 1.49444455e+00 1 -4.37349177e-01 7.85783578e-02 1.50525038e+00 | -4.37349177e-01 7.85783578e-02 1.50525038e+00 2 -5.80181155e-01 -2.10283968e-01 -1.73147037e+00 | -5.80181155e-01 -2.10283968e-01 -1.73147037e+00 3 4.38643297e-01 1.01302103e-01 -1.26822457e+00 | 4.38643297e-01 1.01302103e-01 -1.26822457e+00 4 5.78887034e-01 3.04035069e-02 1.49444455e+00 | 5.78887034e-01 3.04035069e-02 1.49444455e+00 5 -4.37349177e-01 7.85783578e-02 1.50525038e+00 | -4.37349177e-01 7.85783578e-02 1.50525038e+00 6 -5.80181155e-01 -2.10283968e-01 -1.73147037e+00 | -5.80181155e-01 -2.10283968e-01 -1.73147037e+00 7 4.38643297e-01 1.01302103e-01 -1.26822457e+00 | 4.38643297e-01 1.01302103e-01 -1.26822457e+00 8 5.78887034e-01 3.04035069e-02 1.49444455e+00 | 5.78887034e-01 3.04035069e-02 1.49444455e+00 9 -4.37349177e-01 7.85783578e-02 1.50525038e+00 | -4.37349177e-01 7.85783578e-02 1.50525038e+00 10 -5.80181155e-01 -2.10283968e-01 -1.73147037e+00 | -5.80181155e-01 -2.10283968e-01 -1.73147037e+00 11 4.38643297e-01 1.01302103e-01 -1.26822457e+00 | 4.38643297e-01 1.01302103e-01 -1.26822457e+00 12 5.78887034e-01 3.04035069e-02 1.49444455e+00 | 5.78887034e-01 3.04035069e-02 1.49444455e+00 13 -4.37349177e-01 7.85783578e-02 1.50525038e+00 | -4.37349177e-01 7.85783578e-02 1.50525038e+00 14 -5.80181155e-01 -2.10283968e-01 -1.73147037e+00 | -5.80181155e-01 -2.10283968e-01 -1.73147037e+00 15 4.38643297e-01 1.01302103e-01 -1.26822457e+00 | 4.38643297e-01 1.01302103e-01 -1.26822457e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = TFT (Configuration in file "config-He-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = -13.069726465798587 2^p V(r_1,...,r_N) = -13.069726465798576 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 2.76109066e-03 1.63702354e+00 2.61077365e-01 | 2.76109066e-03 1.63702354e+00 2.61077365e-01 1 3.21565756e-01 -1.70626698e+00 2.55499277e-01 | 3.21565756e-01 -1.70626698e+00 2.55499277e-01 2 3.42518948e-02 1.55830335e+00 -3.46750509e-01 | 3.42518948e-02 1.55830335e+00 -3.46750509e-01 3 -3.58578741e-01 -1.48905990e+00 -1.69826134e-01 | -3.58578741e-01 -1.48905990e+00 -1.69826134e-01 4 2.76109066e-03 1.63702354e+00 2.61077365e-01 | 2.76109066e-03 1.63702354e+00 2.61077365e-01 5 3.21565756e-01 -1.70626698e+00 2.55499277e-01 | 3.21565756e-01 -1.70626698e+00 2.55499277e-01 6 3.42518948e-02 1.55830335e+00 -3.46750509e-01 | 3.42518948e-02 1.55830335e+00 -3.46750509e-01 7 -3.58578741e-01 -1.48905990e+00 -1.69826134e-01 | -3.58578741e-01 -1.48905990e+00 -1.69826134e-01 8 2.76109066e-03 1.63702354e+00 2.61077365e-01 | 2.76109066e-03 1.63702354e+00 2.61077365e-01 9 3.21565756e-01 -1.70626698e+00 2.55499277e-01 | 3.21565756e-01 -1.70626698e+00 2.55499277e-01 10 3.42518948e-02 1.55830335e+00 -3.46750509e-01 | 3.42518948e-02 1.55830335e+00 -3.46750509e-01 11 -3.58578741e-01 -1.48905990e+00 -1.69826134e-01 | -3.58578741e-01 -1.48905990e+00 -1.69826134e-01 12 2.76109066e-03 1.63702354e+00 2.61077365e-01 | 2.76109066e-03 1.63702354e+00 2.61077365e-01 13 3.21565756e-01 -1.70626698e+00 2.55499277e-01 | 3.21565756e-01 -1.70626698e+00 2.55499277e-01 14 3.42518948e-02 1.55830335e+00 -3.46750509e-01 | 3.42518948e-02 1.55830335e+00 -3.46750509e-01 15 -3.58578741e-01 -1.48905990e+00 -1.69826134e-01 | -3.58578741e-01 -1.48905990e+00 -1.69826134e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = TFF (Configuration in file "config-He-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = -5.724884070679707 2^p V(r_1,...,r_N) = -5.724884070679708 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 1.01952411e-01 1.16357425e+00 1.10830661e+00 | 1.01952411e-01 1.16357425e+00 1.10830661e+00 1 -2.33202600e-02 -1.24373765e+00 1.27711775e+00 | -2.33202600e-02 -1.24373765e+00 1.27711775e+00 2 -2.24395323e-01 1.34949999e+00 -1.52520666e+00 | -2.24395323e-01 1.34949999e+00 -1.52520666e+00 3 1.45763172e-01 -1.26933659e+00 -8.60217703e-01 | 1.45763172e-01 -1.26933659e+00 -8.60217703e-01 4 1.01952411e-01 1.16357425e+00 1.10830661e+00 | 1.01952411e-01 1.16357425e+00 1.10830661e+00 5 -2.33202600e-02 -1.24373765e+00 1.27711775e+00 | -2.33202600e-02 -1.24373765e+00 1.27711775e+00 6 -2.24395323e-01 1.34949999e+00 -1.52520666e+00 | -2.24395323e-01 1.34949999e+00 -1.52520666e+00 7 1.45763172e-01 -1.26933659e+00 -8.60217703e-01 | 1.45763172e-01 -1.26933659e+00 -8.60217703e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = FTT (Configuration in file "config-He-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = -10.095293541078249 2^p V(r_1,...,r_N) = -10.095293541078245 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 1.39548553e+00 4.22066385e-01 4.90505180e-01 | 1.39548553e+00 4.22066385e-01 4.90505180e-01 1 -1.36435305e+00 -2.90550947e-01 4.64305604e-01 | -1.36435305e+00 -2.90550947e-01 4.64305604e-01 2 -1.40202592e+00 2.22195016e-01 -4.78929099e-01 | -1.40202592e+00 2.22195016e-01 -4.78929099e-01 3 1.37089344e+00 -3.53710454e-01 -4.75881685e-01 | 1.37089344e+00 -3.53710454e-01 -4.75881685e-01 4 1.39548553e+00 4.22066385e-01 4.90505180e-01 | 1.39548553e+00 4.22066385e-01 4.90505180e-01 5 -1.36435305e+00 -2.90550947e-01 4.64305604e-01 | -1.36435305e+00 -2.90550947e-01 4.64305604e-01 6 -1.40202592e+00 2.22195016e-01 -4.78929099e-01 | -1.40202592e+00 2.22195016e-01 -4.78929099e-01 7 1.37089344e+00 -3.53710454e-01 -4.75881685e-01 | 1.37089344e+00 -3.53710454e-01 -4.75881685e-01 8 1.39548553e+00 4.22066385e-01 4.90505180e-01 | 1.39548553e+00 4.22066385e-01 4.90505180e-01 9 -1.36435305e+00 -2.90550947e-01 4.64305604e-01 | -1.36435305e+00 -2.90550947e-01 4.64305604e-01 10 -1.40202592e+00 2.22195016e-01 -4.78929099e-01 | -1.40202592e+00 2.22195016e-01 -4.78929099e-01 11 1.37089344e+00 -3.53710454e-01 -4.75881685e-01 | 1.37089344e+00 -3.53710454e-01 -4.75881685e-01 12 1.39548553e+00 4.22066385e-01 4.90505180e-01 | 1.39548553e+00 4.22066385e-01 4.90505180e-01 13 -1.36435305e+00 -2.90550947e-01 4.64305604e-01 | -1.36435305e+00 -2.90550947e-01 4.64305604e-01 14 -1.40202592e+00 2.22195016e-01 -4.78929099e-01 | -1.40202592e+00 2.22195016e-01 -4.78929099e-01 15 1.37089344e+00 -3.53710454e-01 -4.75881685e-01 | 1.37089344e+00 -3.53710454e-01 -4.75881685e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = FTF (Configuration in file "config-He-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = -5.5271866013752735 2^p V(r_1,...,r_N) = -5.5271866013752735 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 1.30943027e+00 2.46270410e-02 1.36523163e+00 | 1.30943027e+00 2.46270410e-02 1.36523163e+00 1 -1.37641688e+00 1.98587948e-01 9.63225178e-01 | -1.37641688e+00 1.98587948e-01 9.63225178e-01 2 -1.26446835e+00 -8.44288038e-02 -1.08837356e+00 | -1.26446835e+00 -8.44288038e-02 -1.08837356e+00 3 1.33145496e+00 -1.38786185e-01 -1.24008325e+00 | 1.33145496e+00 -1.38786185e-01 -1.24008325e+00 4 1.30943027e+00 2.46270410e-02 1.36523163e+00 | 1.30943027e+00 2.46270410e-02 1.36523163e+00 5 -1.37641688e+00 1.98587948e-01 9.63225178e-01 | -1.37641688e+00 1.98587948e-01 9.63225178e-01 6 -1.26446835e+00 -8.44288038e-02 -1.08837356e+00 | -1.26446835e+00 -8.44288038e-02 -1.08837356e+00 7 1.33145496e+00 -1.38786185e-01 -1.24008325e+00 | 1.33145496e+00 -1.38786185e-01 -1.24008325e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = He, PBC = FFT (Configuration in file "config-He-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = -4.364720562520066 2^p V(r_1,...,r_N) = -4.364720562520066 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 1.15472238e+00 9.06413219e-01 2.69236701e-01 | 1.15472238e+00 9.06413219e-01 2.69236701e-01 1 -9.55529573e-01 -1.26396813e+00 -1.89067695e-01 | -9.55529573e-01 -1.26396813e+00 -1.89067695e-01 2 -1.21621951e+00 1.11708028e+00 1.67064748e-01 | -1.21621951e+00 1.11708028e+00 1.67064748e-01 3 1.01702671e+00 -7.59525372e-01 -2.47233754e-01 | 1.01702671e+00 -7.59525372e-01 -2.47233754e-01 4 1.15472238e+00 9.06413219e-01 2.69236701e-01 | 1.15472238e+00 9.06413219e-01 2.69236701e-01 5 -9.55529573e-01 -1.26396813e+00 -1.89067695e-01 | -9.55529573e-01 -1.26396813e+00 -1.89067695e-01 6 -1.21621951e+00 1.11708028e+00 1.67064748e-01 | -1.21621951e+00 1.11708028e+00 1.67064748e-01 7 1.01702671e+00 -7.59525372e-01 -2.47233754e-01 | 1.01702671e+00 -7.59525372e-01 -2.47233754e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = TTT (Configuration in file "config-W-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 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)) = 260.04775957507485 2^p V(r_1,...,r_N) = 260.04775957507513 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 -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 | -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 1 1.25388039e+01 1.14418985e+01 -2.69889249e+01 | 1.25388039e+01 1.14418985e+01 -2.69889249e+01 2 1.56651460e+01 -4.35640410e+00 1.47283677e+01 | 1.56651460e+01 -4.35640410e+00 1.47283677e+01 3 -1.77807359e+01 8.10248318e+00 2.55962905e+01 | -1.77807359e+01 8.10248318e+00 2.55962905e+01 4 -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 | -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 5 1.25388039e+01 1.14418985e+01 -2.69889249e+01 | 1.25388039e+01 1.14418985e+01 -2.69889249e+01 6 1.56651460e+01 -4.35640410e+00 1.47283677e+01 | 1.56651460e+01 -4.35640410e+00 1.47283677e+01 7 -1.77807359e+01 8.10248318e+00 2.55962905e+01 | -1.77807359e+01 8.10248318e+00 2.55962905e+01 8 -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 | -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 9 1.25388039e+01 1.14418985e+01 -2.69889249e+01 | 1.25388039e+01 1.14418985e+01 -2.69889249e+01 10 1.56651460e+01 -4.35640410e+00 1.47283677e+01 | 1.56651460e+01 -4.35640410e+00 1.47283677e+01 11 -1.77807359e+01 8.10248318e+00 2.55962905e+01 | -1.77807359e+01 8.10248318e+00 2.55962905e+01 12 -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 | -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 13 1.25388039e+01 1.14418985e+01 -2.69889249e+01 | 1.25388039e+01 1.14418985e+01 -2.69889249e+01 14 1.56651460e+01 -4.35640410e+00 1.47283677e+01 | 1.56651460e+01 -4.35640410e+00 1.47283677e+01 15 -1.77807359e+01 8.10248318e+00 2.55962905e+01 | -1.77807359e+01 8.10248318e+00 2.55962905e+01 16 -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 | -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 17 1.25388039e+01 1.14418985e+01 -2.69889249e+01 | 1.25388039e+01 1.14418985e+01 -2.69889249e+01 18 1.56651460e+01 -4.35640410e+00 1.47283677e+01 | 1.56651460e+01 -4.35640410e+00 1.47283677e+01 19 -1.77807359e+01 8.10248318e+00 2.55962905e+01 | -1.77807359e+01 8.10248318e+00 2.55962905e+01 20 -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 | -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 21 1.25388039e+01 1.14418985e+01 -2.69889249e+01 | 1.25388039e+01 1.14418985e+01 -2.69889249e+01 22 1.56651460e+01 -4.35640410e+00 1.47283677e+01 | 1.56651460e+01 -4.35640410e+00 1.47283677e+01 23 -1.77807359e+01 8.10248318e+00 2.55962905e+01 | -1.77807359e+01 8.10248318e+00 2.55962905e+01 24 -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 | -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 25 1.25388039e+01 1.14418985e+01 -2.69889249e+01 | 1.25388039e+01 1.14418985e+01 -2.69889249e+01 26 1.56651460e+01 -4.35640410e+00 1.47283677e+01 | 1.56651460e+01 -4.35640410e+00 1.47283677e+01 27 -1.77807359e+01 8.10248318e+00 2.55962905e+01 | -1.77807359e+01 8.10248318e+00 2.55962905e+01 28 -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 | -1.04232140e+01 -1.51879776e+01 -1.33357334e+01 29 1.25388039e+01 1.14418985e+01 -2.69889249e+01 | 1.25388039e+01 1.14418985e+01 -2.69889249e+01 30 1.56651460e+01 -4.35640410e+00 1.47283677e+01 | 1.56651460e+01 -4.35640410e+00 1.47283677e+01 31 -1.77807359e+01 8.10248318e+00 2.55962905e+01 | -1.77807359e+01 8.10248318e+00 2.55962905e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = TTF (Configuration in file "config-W-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 76.52216783578349 2^p V(r_1,...,r_N) = 76.52216783578339 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 -6.98640419e+00 -1.26386051e+01 -3.80570835e+01 | -6.98640419e+00 -1.26386051e+01 -3.80570835e+01 1 1.58882532e+01 1.21904570e+01 -3.71971891e+01 | 1.58882532e+01 1.21904570e+01 -3.71971891e+01 2 -4.45883975e+00 -1.22078808e+01 3.63572370e+01 | -4.45883975e+00 -1.22078808e+01 3.63572370e+01 3 -4.44300925e+00 1.26560288e+01 3.88970356e+01 | -4.44300925e+00 1.26560288e+01 3.88970356e+01 4 -6.98640419e+00 -1.26386051e+01 -3.80570835e+01 | -6.98640419e+00 -1.26386051e+01 -3.80570835e+01 5 1.58882532e+01 1.21904570e+01 -3.71971891e+01 | 1.58882532e+01 1.21904570e+01 -3.71971891e+01 6 -4.45883975e+00 -1.22078808e+01 3.63572370e+01 | -4.45883975e+00 -1.22078808e+01 3.63572370e+01 7 -4.44300925e+00 1.26560288e+01 3.88970356e+01 | -4.44300925e+00 1.26560288e+01 3.88970356e+01 8 -6.98640419e+00 -1.26386051e+01 -3.80570835e+01 | -6.98640419e+00 -1.26386051e+01 -3.80570835e+01 9 1.58882532e+01 1.21904570e+01 -3.71971891e+01 | 1.58882532e+01 1.21904570e+01 -3.71971891e+01 10 -4.45883975e+00 -1.22078808e+01 3.63572370e+01 | -4.45883975e+00 -1.22078808e+01 3.63572370e+01 11 -4.44300925e+00 1.26560288e+01 3.88970356e+01 | -4.44300925e+00 1.26560288e+01 3.88970356e+01 12 -6.98640419e+00 -1.26386051e+01 -3.80570835e+01 | -6.98640419e+00 -1.26386051e+01 -3.80570835e+01 13 1.58882532e+01 1.21904570e+01 -3.71971891e+01 | 1.58882532e+01 1.21904570e+01 -3.71971891e+01 14 -4.45883975e+00 -1.22078808e+01 3.63572370e+01 | -4.45883975e+00 -1.22078808e+01 3.63572370e+01 15 -4.44300925e+00 1.26560288e+01 3.88970356e+01 | -4.44300925e+00 1.26560288e+01 3.88970356e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = TFT (Configuration in file "config-W-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 44.22729570062544 2^p V(r_1,...,r_N) = 44.22729570062541 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 8.57551537e+00 -3.10857155e+01 4.49532697e+00 | 8.57551537e+00 -3.10857155e+01 4.49532697e+00 1 8.29549079e+00 3.20798002e+01 -3.14032937e+00 | 8.29549079e+00 3.20798002e+01 -3.14032937e+00 2 -1.03951978e+01 -3.01347378e+01 -9.70375668e+00 | -1.03951978e+01 -3.01347378e+01 -9.70375668e+00 3 -6.47580834e+00 2.91406531e+01 8.34875908e+00 | -6.47580834e+00 2.91406531e+01 8.34875908e+00 4 8.57551537e+00 -3.10857155e+01 4.49532697e+00 | 8.57551537e+00 -3.10857155e+01 4.49532697e+00 5 8.29549079e+00 3.20798002e+01 -3.14032937e+00 | 8.29549079e+00 3.20798002e+01 -3.14032937e+00 6 -1.03951978e+01 -3.01347378e+01 -9.70375668e+00 | -1.03951978e+01 -3.01347378e+01 -9.70375668e+00 7 -6.47580834e+00 2.91406531e+01 8.34875908e+00 | -6.47580834e+00 2.91406531e+01 8.34875908e+00 8 8.57551537e+00 -3.10857155e+01 4.49532697e+00 | 8.57551537e+00 -3.10857155e+01 4.49532697e+00 9 8.29549079e+00 3.20798002e+01 -3.14032937e+00 | 8.29549079e+00 3.20798002e+01 -3.14032937e+00 10 -1.03951978e+01 -3.01347378e+01 -9.70375668e+00 | -1.03951978e+01 -3.01347378e+01 -9.70375668e+00 11 -6.47580834e+00 2.91406531e+01 8.34875908e+00 | -6.47580834e+00 2.91406531e+01 8.34875908e+00 12 8.57551537e+00 -3.10857155e+01 4.49532697e+00 | 8.57551537e+00 -3.10857155e+01 4.49532697e+00 13 8.29549079e+00 3.20798002e+01 -3.14032937e+00 | 8.29549079e+00 3.20798002e+01 -3.14032937e+00 14 -1.03951978e+01 -3.01347378e+01 -9.70375668e+00 | -1.03951978e+01 -3.01347378e+01 -9.70375668e+00 15 -6.47580834e+00 2.91406531e+01 8.34875908e+00 | -6.47580834e+00 2.91406531e+01 8.34875908e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = TFF (Configuration in file "config-W-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 34.6312814869407 2^p V(r_1,...,r_N) = 34.63128148694076 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 1.47353710e+01 -3.15614950e+01 -3.43315604e+01 | 1.47353710e+01 -3.15614950e+01 -3.43315604e+01 1 -1.59414019e+01 3.67837161e+01 -3.19261333e+01 | -1.59414019e+01 3.67837161e+01 -3.19261333e+01 2 -1.48208915e+01 -3.70476600e+01 3.16382642e+01 | -1.48208915e+01 -3.70476600e+01 3.16382642e+01 3 1.60269224e+01 3.18254389e+01 3.46194295e+01 | 1.60269224e+01 3.18254389e+01 3.46194295e+01 4 1.47353710e+01 -3.15614950e+01 -3.43315604e+01 | 1.47353710e+01 -3.15614950e+01 -3.43315604e+01 5 -1.59414019e+01 3.67837161e+01 -3.19261333e+01 | -1.59414019e+01 3.67837161e+01 -3.19261333e+01 6 -1.48208915e+01 -3.70476600e+01 3.16382642e+01 | -1.48208915e+01 -3.70476600e+01 3.16382642e+01 7 1.60269224e+01 3.18254389e+01 3.46194295e+01 | 1.60269224e+01 3.18254389e+01 3.46194295e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = FTT (Configuration in file "config-W-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 241.1162880279044 2^p V(r_1,...,r_N) = 241.11628802790455 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 -4.95074136e+01 -1.25841205e+01 -4.03281012e+01 | -4.95074136e+01 -1.25841205e+01 -4.03281012e+01 1 5.18186691e+01 1.56026154e+01 -3.56185469e+01 | 5.18186691e+01 1.56026154e+01 -3.56185469e+01 2 4.94063319e+01 -1.31053769e+01 4.11251194e+01 | 4.94063319e+01 -1.31053769e+01 4.11251194e+01 3 -5.17175875e+01 1.00868821e+01 3.48215287e+01 | -5.17175875e+01 1.00868821e+01 3.48215287e+01 4 -4.95074136e+01 -1.25841205e+01 -4.03281012e+01 | -4.95074136e+01 -1.25841205e+01 -4.03281012e+01 5 5.18186691e+01 1.56026154e+01 -3.56185469e+01 | 5.18186691e+01 1.56026154e+01 -3.56185469e+01 6 4.94063319e+01 -1.31053769e+01 4.11251194e+01 | 4.94063319e+01 -1.31053769e+01 4.11251194e+01 7 -5.17175875e+01 1.00868821e+01 3.48215287e+01 | -5.17175875e+01 1.00868821e+01 3.48215287e+01 8 -4.95074136e+01 -1.25841205e+01 -4.03281012e+01 | -4.95074136e+01 -1.25841205e+01 -4.03281012e+01 9 5.18186691e+01 1.56026154e+01 -3.56185469e+01 | 5.18186691e+01 1.56026154e+01 -3.56185469e+01 10 4.94063319e+01 -1.31053769e+01 4.11251194e+01 | 4.94063319e+01 -1.31053769e+01 4.11251194e+01 11 -5.17175875e+01 1.00868821e+01 3.48215287e+01 | -5.17175875e+01 1.00868821e+01 3.48215287e+01 12 -4.95074136e+01 -1.25841205e+01 -4.03281012e+01 | -4.95074136e+01 -1.25841205e+01 -4.03281012e+01 13 5.18186691e+01 1.56026154e+01 -3.56185469e+01 | 5.18186691e+01 1.56026154e+01 -3.56185469e+01 14 4.94063319e+01 -1.31053769e+01 4.11251194e+01 | 4.94063319e+01 -1.31053769e+01 4.11251194e+01 15 -5.17175875e+01 1.00868821e+01 3.48215287e+01 | -5.17175875e+01 1.00868821e+01 3.48215287e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = FTF (Configuration in file "config-W-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 27.934851234956284 2^p V(r_1,...,r_N) = 27.93485123495625 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 -3.35083279e+01 -1.83291150e+01 -2.97150777e+01 | -3.35083279e+01 -1.83291150e+01 -2.97150777e+01 1 2.65028005e+01 1.87038763e+01 -3.31831263e+01 | 2.65028005e+01 1.87038763e+01 -3.31831263e+01 2 3.63899173e+01 -2.05665650e+01 2.90006654e+01 | 3.63899173e+01 -2.05665650e+01 2.90006654e+01 3 -2.93843899e+01 2.01918038e+01 3.38975386e+01 | -2.93843899e+01 2.01918038e+01 3.38975386e+01 4 -3.35083279e+01 -1.83291150e+01 -2.97150777e+01 | -3.35083279e+01 -1.83291150e+01 -2.97150777e+01 5 2.65028005e+01 1.87038763e+01 -3.31831263e+01 | 2.65028005e+01 1.87038763e+01 -3.31831263e+01 6 3.63899173e+01 -2.05665650e+01 2.90006654e+01 | 3.63899173e+01 -2.05665650e+01 2.90006654e+01 7 -2.93843899e+01 2.01918038e+01 3.38975386e+01 | -2.93843899e+01 2.01918038e+01 3.38975386e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = W, PBC = FFT (Configuration in file "config-W-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 67.9643743520168 2^p V(r_1,...,r_N) = 67.96437435201683 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 -4.14805864e+01 -3.39578302e+01 7.50861827e+00 | -4.14805864e+01 -3.39578302e+01 7.50861827e+00 1 3.88689532e+01 3.36208471e+01 6.61692975e+00 | 3.88689532e+01 3.36208471e+01 6.61692975e+00 2 3.65129148e+01 -4.41632836e+01 -9.54266543e+00 | 3.65129148e+01 -4.41632836e+01 -9.54266543e+00 3 -3.39012816e+01 4.45002667e+01 -4.58288259e+00 | -3.39012816e+01 4.45002667e+01 -4.58288259e+00 4 -4.14805864e+01 -3.39578302e+01 7.50861827e+00 | -4.14805864e+01 -3.39578302e+01 7.50861827e+00 5 3.88689532e+01 3.36208471e+01 6.61692975e+00 | 3.88689532e+01 3.36208471e+01 6.61692975e+00 6 3.65129148e+01 -4.41632836e+01 -9.54266543e+00 | 3.65129148e+01 -4.41632836e+01 -9.54266543e+00 7 -3.39012816e+01 4.45002667e+01 -4.58288259e+00 | -3.39012816e+01 4.45002667e+01 -4.58288259e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = TTT (Configuration in file "config-HHeW-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=3 periodic directions, which means an increase by a factor n=2^3=8 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)) = -13.15220067022643 2^p V(r_1,...,r_N) = -13.152200670226236 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 3.60368281e+00 3.45769292e+00 1.14011546e+00 | 3.60368281e+00 3.45769292e+00 1.14011546e+00 1 -5.65915230e+00 -2.45301245e+00 1.54300351e+00 | -5.65915230e+00 -2.45301245e+00 1.54300351e+00 2 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 | 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 3 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 | 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 4 3.60368281e+00 3.45769292e+00 1.14011546e+00 | 3.60368281e+00 3.45769292e+00 1.14011546e+00 5 -5.65915230e+00 -2.45301245e+00 1.54300351e+00 | -5.65915230e+00 -2.45301245e+00 1.54300351e+00 6 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 | 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 7 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 | 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 8 3.60368281e+00 3.45769292e+00 1.14011546e+00 | 3.60368281e+00 3.45769292e+00 1.14011546e+00 9 -5.65915230e+00 -2.45301245e+00 1.54300351e+00 | -5.65915230e+00 -2.45301245e+00 1.54300351e+00 10 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 | 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 11 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 | 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 12 3.60368281e+00 3.45769292e+00 1.14011546e+00 | 3.60368281e+00 3.45769292e+00 1.14011546e+00 13 -5.65915230e+00 -2.45301245e+00 1.54300351e+00 | -5.65915230e+00 -2.45301245e+00 1.54300351e+00 14 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 | 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 15 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 | 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 16 3.60368281e+00 3.45769292e+00 1.14011546e+00 | 3.60368281e+00 3.45769292e+00 1.14011546e+00 17 -5.65915230e+00 -2.45301245e+00 1.54300351e+00 | -5.65915230e+00 -2.45301245e+00 1.54300351e+00 18 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 | 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 19 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 | 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 20 3.60368281e+00 3.45769292e+00 1.14011546e+00 | 3.60368281e+00 3.45769292e+00 1.14011546e+00 21 -5.65915230e+00 -2.45301245e+00 1.54300351e+00 | -5.65915230e+00 -2.45301245e+00 1.54300351e+00 22 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 | 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 23 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 | 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 24 3.60368281e+00 3.45769292e+00 1.14011546e+00 | 3.60368281e+00 3.45769292e+00 1.14011546e+00 25 -5.65915230e+00 -2.45301245e+00 1.54300351e+00 | -5.65915230e+00 -2.45301245e+00 1.54300351e+00 26 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 | 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 27 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 | 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 28 3.60368281e+00 3.45769292e+00 1.14011546e+00 | 3.60368281e+00 3.45769292e+00 1.14011546e+00 29 -5.65915230e+00 -2.45301245e+00 1.54300351e+00 | -5.65915230e+00 -2.45301245e+00 1.54300351e+00 30 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 | 2.08270289e-02 -3.01779480e-01 -2.32548221e-01 31 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 | 2.03464246e+00 -7.02900994e-01 -2.45057074e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = TTF (Configuration in file "config-HHeW-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = -12.21443721553932 2^p V(r_1,...,r_N) = -12.214437215539288 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 -2.86295541e-01 -6.67595747e-01 -3.12406994e+00 | -2.86295541e-01 -6.67595747e-01 -3.12406994e+00 1 5.57727196e-01 6.25100590e-01 -3.05598954e-01 | 5.57727196e-01 6.25100590e-01 -3.05598954e-01 2 5.99386443e-01 -1.06377534e-01 1.28205159e+00 | 5.99386443e-01 -1.06377534e-01 1.28205159e+00 3 -8.70818098e-01 1.48872691e-01 2.14761730e+00 | -8.70818098e-01 1.48872691e-01 2.14761730e+00 4 -2.86295541e-01 -6.67595747e-01 -3.12406994e+00 | -2.86295541e-01 -6.67595747e-01 -3.12406994e+00 5 5.57727196e-01 6.25100590e-01 -3.05598954e-01 | 5.57727196e-01 6.25100590e-01 -3.05598954e-01 6 5.99386443e-01 -1.06377534e-01 1.28205159e+00 | 5.99386443e-01 -1.06377534e-01 1.28205159e+00 7 -8.70818098e-01 1.48872691e-01 2.14761730e+00 | -8.70818098e-01 1.48872691e-01 2.14761730e+00 8 -2.86295541e-01 -6.67595747e-01 -3.12406994e+00 | -2.86295541e-01 -6.67595747e-01 -3.12406994e+00 9 5.57727196e-01 6.25100590e-01 -3.05598954e-01 | 5.57727196e-01 6.25100590e-01 -3.05598954e-01 10 5.99386443e-01 -1.06377534e-01 1.28205159e+00 | 5.99386443e-01 -1.06377534e-01 1.28205159e+00 11 -8.70818098e-01 1.48872691e-01 2.14761730e+00 | -8.70818098e-01 1.48872691e-01 2.14761730e+00 12 -2.86295541e-01 -6.67595747e-01 -3.12406994e+00 | -2.86295541e-01 -6.67595747e-01 -3.12406994e+00 13 5.57727196e-01 6.25100590e-01 -3.05598954e-01 | 5.57727196e-01 6.25100590e-01 -3.05598954e-01 14 5.99386443e-01 -1.06377534e-01 1.28205159e+00 | 5.99386443e-01 -1.06377534e-01 1.28205159e+00 15 -8.70818098e-01 1.48872691e-01 2.14761730e+00 | -8.70818098e-01 1.48872691e-01 2.14761730e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = TFT (Configuration in file "config-HHeW-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = -12.071955884744982 2^p V(r_1,...,r_N) = -12.071955884744952 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 -1.33569629e+00 -9.83986866e-01 -1.14677618e+00 | -1.33569629e+00 -9.83986866e-01 -1.14677618e+00 1 -5.84961332e-01 1.90868270e-01 -4.95798394e-01 | -5.84961332e-01 1.90868270e-01 -4.95798394e-01 2 1.14879967e+00 -2.15952296e+00 4.39511768e-01 | 1.14879967e+00 -2.15952296e+00 4.39511768e-01 3 7.71857944e-01 2.95264156e+00 1.20306281e+00 | 7.71857944e-01 2.95264156e+00 1.20306281e+00 4 -1.33569629e+00 -9.83986866e-01 -1.14677618e+00 | -1.33569629e+00 -9.83986866e-01 -1.14677618e+00 5 -5.84961332e-01 1.90868270e-01 -4.95798394e-01 | -5.84961332e-01 1.90868270e-01 -4.95798394e-01 6 1.14879967e+00 -2.15952296e+00 4.39511768e-01 | 1.14879967e+00 -2.15952296e+00 4.39511768e-01 7 7.71857944e-01 2.95264156e+00 1.20306281e+00 | 7.71857944e-01 2.95264156e+00 1.20306281e+00 8 -1.33569629e+00 -9.83986866e-01 -1.14677618e+00 | -1.33569629e+00 -9.83986866e-01 -1.14677618e+00 9 -5.84961332e-01 1.90868270e-01 -4.95798394e-01 | -5.84961332e-01 1.90868270e-01 -4.95798394e-01 10 1.14879967e+00 -2.15952296e+00 4.39511768e-01 | 1.14879967e+00 -2.15952296e+00 4.39511768e-01 11 7.71857944e-01 2.95264156e+00 1.20306281e+00 | 7.71857944e-01 2.95264156e+00 1.20306281e+00 12 -1.33569629e+00 -9.83986866e-01 -1.14677618e+00 | -1.33569629e+00 -9.83986866e-01 -1.14677618e+00 13 -5.84961332e-01 1.90868270e-01 -4.95798394e-01 | -5.84961332e-01 1.90868270e-01 -4.95798394e-01 14 1.14879967e+00 -2.15952296e+00 4.39511768e-01 | 1.14879967e+00 -2.15952296e+00 4.39511768e-01 15 7.71857944e-01 2.95264156e+00 1.20306281e+00 | 7.71857944e-01 2.95264156e+00 1.20306281e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = TFF (Configuration in file "config-HHeW-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = 0.48581480272215244 2^p V(r_1,...,r_N) = 0.4858148027221544 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 -6.28061998e+00 -1.87995301e+00 -8.89652596e+00 | -6.28061998e+00 -1.87995301e+00 -8.89652596e+00 1 2.56594395e+00 1.47121018e-01 -2.51913489e+00 | 2.56594395e+00 1.47121018e-01 -2.51913489e+00 2 6.50395730e+00 -2.72369913e+00 8.85209102e+00 | 6.50395730e+00 -2.72369913e+00 8.85209102e+00 3 -2.78928128e+00 4.45653113e+00 2.56356983e+00 | -2.78928128e+00 4.45653113e+00 2.56356983e+00 4 -6.28061998e+00 -1.87995301e+00 -8.89652596e+00 | -6.28061998e+00 -1.87995301e+00 -8.89652596e+00 5 2.56594395e+00 1.47121018e-01 -2.51913489e+00 | 2.56594395e+00 1.47121018e-01 -2.51913489e+00 6 6.50395730e+00 -2.72369913e+00 8.85209102e+00 | 6.50395730e+00 -2.72369913e+00 8.85209102e+00 7 -2.78928128e+00 4.45653113e+00 2.56356983e+00 | -2.78928128e+00 4.45653113e+00 2.56356983e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = FTT (Configuration in file "config-HHeW-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=2 periodic directions, which means an increase by a factor n=2^2=4 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)) = 0.9813731346747068 2^p V(r_1,...,r_N) = 0.9813731346747214 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 -3.95363624e-01 -7.96930298e-01 5.73158666e-01 | -3.95363624e-01 -7.96930298e-01 5.73158666e-01 1 6.26195158e+00 -9.90010761e-01 -9.47449453e+00 | 6.26195158e+00 -9.90010761e-01 -9.47449453e+00 2 3.58613976e+00 2.95508684e+00 3.36647508e+00 | 3.58613976e+00 2.95508684e+00 3.36647508e+00 3 -9.45272771e+00 -1.16814578e+00 5.53486079e+00 | -9.45272771e+00 -1.16814578e+00 5.53486079e+00 4 -3.95363624e-01 -7.96930298e-01 5.73158666e-01 | -3.95363624e-01 -7.96930298e-01 5.73158666e-01 5 6.26195158e+00 -9.90010761e-01 -9.47449453e+00 | 6.26195158e+00 -9.90010761e-01 -9.47449453e+00 6 3.58613976e+00 2.95508684e+00 3.36647508e+00 | 3.58613976e+00 2.95508684e+00 3.36647508e+00 7 -9.45272771e+00 -1.16814578e+00 5.53486079e+00 | -9.45272771e+00 -1.16814578e+00 5.53486079e+00 8 -3.95363624e-01 -7.96930298e-01 5.73158666e-01 | -3.95363624e-01 -7.96930298e-01 5.73158666e-01 9 6.26195158e+00 -9.90010761e-01 -9.47449453e+00 | 6.26195158e+00 -9.90010761e-01 -9.47449453e+00 10 3.58613976e+00 2.95508684e+00 3.36647508e+00 | 3.58613976e+00 2.95508684e+00 3.36647508e+00 11 -9.45272771e+00 -1.16814578e+00 5.53486079e+00 | -9.45272771e+00 -1.16814578e+00 5.53486079e+00 12 -3.95363624e-01 -7.96930298e-01 5.73158666e-01 | -3.95363624e-01 -7.96930298e-01 5.73158666e-01 13 6.26195158e+00 -9.90010761e-01 -9.47449453e+00 | 6.26195158e+00 -9.90010761e-01 -9.47449453e+00 14 3.58613976e+00 2.95508684e+00 3.36647508e+00 | 3.58613976e+00 2.95508684e+00 3.36647508e+00 15 -9.45272771e+00 -1.16814578e+00 5.53486079e+00 | -9.45272771e+00 -1.16814578e+00 5.53486079e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = FTF (Configuration in file "config-HHeW-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = -2.8125097007438393 2^p V(r_1,...,r_N) = -2.812509700743839 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 -1.23211509e-01 -9.08828580e-02 -7.06416390e-01 | -1.23211509e-01 -9.08828580e-02 -7.06416390e-01 1 5.92364440e-01 6.80030486e-01 -4.46163596e+00 | 5.92364440e-01 6.80030486e-01 -4.46163596e+00 2 3.91694790e+00 -2.93855369e+00 3.40394252e+00 | 3.91694790e+00 -2.93855369e+00 3.40394252e+00 3 -4.38610083e+00 2.34940606e+00 1.76410983e+00 | -4.38610083e+00 2.34940606e+00 1.76410983e+00 4 -1.23211509e-01 -9.08828580e-02 -7.06416390e-01 | -1.23211509e-01 -9.08828580e-02 -7.06416390e-01 5 5.92364440e-01 6.80030486e-01 -4.46163596e+00 | 5.92364440e-01 6.80030486e-01 -4.46163596e+00 6 3.91694790e+00 -2.93855369e+00 3.40394252e+00 | 3.91694790e+00 -2.93855369e+00 3.40394252e+00 7 -4.38610083e+00 2.34940606e+00 1.76410983e+00 | -4.38610083e+00 2.34940606e+00 1.76410983e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = H He W, PBC = FFT (Configuration in file "config-HHeW-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=1 periodic directions, which means an increase by a factor n=2^1=2 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)) = -4.2974199679653395 2^p V(r_1,...,r_N) = -4.297419967965338 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 -3.19236972e+00 -1.48342789e+00 -6.93871758e-02 | -3.19236972e+00 -1.48342789e+00 -6.93871758e-02 1 1.57010816e+00 7.86906079e-01 -4.95330318e-02 | 1.57010816e+00 7.86906079e-01 -4.95330318e-02 2 1.91878461e+00 2.61936252e-01 7.55778073e-02 | 1.91878461e+00 2.61936252e-01 7.55778073e-02 3 -2.96523046e-01 4.34585558e-01 4.33424003e-02 | -2.96523046e-01 4.34585558e-01 4.33424003e-02 4 -3.19236972e+00 -1.48342789e+00 -6.93871758e-02 | -3.19236972e+00 -1.48342789e+00 -6.93871758e-02 5 1.57010816e+00 7.86906079e-01 -4.95330318e-02 | 1.57010816e+00 7.86906079e-01 -4.95330318e-02 6 1.91878461e+00 2.61936252e-01 7.55778073e-02 | 1.91878461e+00 2.61936252e-01 7.55778073e-02 7 -2.96523046e-01 4.34585558e-01 4.33424003e-02 | -2.96523046e-01 4.34585558e-01 4.33424003e-02 ------------------------------------------------------------------------------------------------------------------------ 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.