A Comparative Review of FEM Like Techniques Applied to the Linear Analysis of Molecular Structures

Abstract

In this study, a historical review of the Finite Element Method (FEM) and Molecular Dynamics (MD), widely used at the macro and nanoscale respectively is presented, emphasizing the actual parallelisms between their development and applications. After this historical introduction, where certain similarities between both methods are pointed out, different FEM-like methods are analyzed and compared as for first order analysis of structures at the nanoscale. Firstly, the Structural Mechanics (SM) approach is analyzed, where it is assumed that the use of Euler Bernoulli beam elements is equivalent to working directly from the force field. On the other hand, the Molecular Element Method (MEM), which provides the stiffness matrices directly from the potentials, is analyzed. Several analytical static cases are studied for the validation and comparison of both methods. Finally, it is shown that, other branch of methods such as Elastic Network Models (ENM) can be viewed as a particular sub-case of the MEM, or as truss-type finite elements. As an example, the analysis of SARS-CoV2 spikes vibrations is included, comparing with both experimental results and continuous models.