The constrained molecular dynamics (CMD) to obtain spatio-temporal memory functions of viscoelastic liquids: stability analysis of equations of motion

Mechanical stress is one of the main characteristics of viscoelastic molecular systems, including vitrifying liquids and amorphous solids which are known to show long-range dynamical heterogeneities. It is therefore important to deal with time- and space-resolved local stress whose correlations can be used to obtain viscoelastic memory functions of such systems, in particular, their wave-vector dependent shear and compression relaxation moduli. However, such memory functions are not directly accessible within standard molecular dynamics (MD) simulations. Here we discuss a new method called the constrained molecular dynamics (CMD) which allows for a direct evaluation of the wave-vector and time dependent viscoelastic moduli. The study is focused, in particular, on the stability analysis of different variants of the CMD, revealing the most efficient stabilization algorithm. Our theoretical predictions for the time-dependence of the most important parameters (like the wave-vector resolved mass current) during the stabilization stage are compared with the simulation data using different CMD algorithms. An excellent agreement is observed, thus confirming the validity of our theoretical approach and its ability to accurately predict the most important initial part of CMD trajectories.