| Abstract: | We propose a new method for calculating the potential of multiparticle interaction. Our method considers the energy symmetry for clusters that contain N identical particles with respect to permutation of the number of atoms and free rotation in three-dimensional space. As an example, we calculate moduli of third-order rigidity for copper considering only the three-particle interaction. We analyze nine models of energy dependence on the polynomials that form the integral rational basis of invariants (IRBI) for the group G 3 = O(3) ? P 3. In this work, we use only the simplest relation between energy and the invariants forming the IRBI: (varepsilon left( {left. {i,k,l} right|j} right) = sumnolimits_{i,k,l} {left[ { - A_1 r_{ik}^{ - 6} + A_2 r_{ik}^{ - 12} + Q_j I_j^{ - n} } right]}), where I j is the invariant number j (j = 1, 2,..., 9). The results are in good agreement with the experimental values. The best agreement is observed at n = 2, j = 4: (I_4 = left( {vec r_{ik} vec r_{kl} } right)left( {vec r_{kl} vec r_{li} } right) + left( {vec r_{kl} vec r_{li} } right)left( {vec r_{li} vec r_{ik} } right) + left( {vec r_{li} vec r_{ik} } right)left( {vec r_{ik} vec r_{kl} } right)). |
