Network theory is used to formulate an atomistic material network. Spectral sparsification is applied to the network as a method for approximating the interatomic forces. Local molecular forces and the total force balance is quantified when the internal forces are approximated. In particular, we compare spectral sparsification to conventional thresholding (radial cut-off distance) of molecular forces for a Lennard-Jones potential and a Coulomb potential. The spectral sparsification for the Lennard-Jones potential yields comparable results while spectral sparsification of the Coulomb potential outperforms the thresholding approach. The results show promising opportunities which may accelerate molecular simulations containing long-range electrical interactions which are relevant to many multifunctional materials.

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