Least square method for the calculation of elastic constants

In this paper, a feasible formula is derived and simplified from least square method to calculate the elastic constants of materials. The simplified equation is identical to the stress and strain fluctuation formula obtained from statistical thermodynamics when the expression of the stress is redefined. It endues the formula with the theoretical validity. On the other hand, the convergence of the formula could be investigated via the theory of numerical analysis. Compared to the traditional fluctuation formula, the new technique shows better universality in the elastic bath method. Results obtained with a nearest-neighbor Lennard-Jones fcc crystal indicate that at low temperature the convergence of the formula is the same as the previous stress and strain fluctuation formula but the symmetry of the elastic constants is improved.