Hello, I was just searching online and discovered this great forum. Please I need help in sorting out a problem with a non-central potential and Newton third law. This is not a physics homework problem. I'm a graduate student working on this equation as a reserch project and there are publications out there using this expression in "Analytical Bond order potential" by Pettiffor et al. They call it Yukawa potential. The form of the potential is: (Sorry for the quakky expressions, I'm not sure if there is an equation editor on this forum, a guide will be appreciated). U_ij = (A/r_ij)* exp(-S_ij(r_ij - r_c)) Where r_ij = sqrt((x_i - X_j)^2 + (y_i - Y_j)^2 + (z_I - z_j)^2) or simply distance between atom i and atom j in cartesian coordinate However, S_ij = 1/2(S_i + S_j) Where; S_i = k_o + (sum(over k not equal to i) exp(-c*r_ik)) similarly S_j = k_o + (sum(over k not equal to j) exp(-c*r_ jk)) Where r_ik and r_ jk are distances from atoms i to atom k and the distance from atom j to atom k respectively. This is the real question. Suppose we have three atoms arranged in a triangle connected to each other where non of the distances between the triangle is the same; that is rij, rjk and rik are not the same. We expect for three body system with no external forces in a closed system to have a conserved force. The forces should sum up to zero; That is F_i = - (F_j + F_k). I'm not sure if I'm doing something wrong here. My problem is that the above energy expression is not giving a conserved forces that sum up to zero, especially when the environment of atoms i and j are different, That is, S_i is not equal l to S_j (when r_ij , r_ik and r_ jk are not all equal) and therefore F_i /= - F_ J so Newton third law of action and reaction are eqaul and opposite is violated. Despite the fact that this force depend only on position, the system does not yield to conservation law. The three atom in a triangle is the most trivial case, but the real problem actually involves many atoms surronding atoms i and j with different densities (S_i and S_ j ) in such a way that the force on atom i due to atom j is affected by other atoms k1_i, k2_i, k3_i, ... kn_i surrounding atom i. While similarly the force on atom j due to atom i is affected by other atoms k1_j, k2_j .....kn_j surrounding atom j. I need to use this potential to derive the forces to perform molecular dynamics simulation and it's been alot of headeache moving forward with this problem as the system will not conserve energy ( Give zero total force) in a close system. Any help will be appreciated. Sorry for my long post, I'm just trying to make things clear. Thanks.