**Abstract**

A molecular dynamics (MD) simulation method has been proposed for three-dimensional (3D) electrorheological complex (dusty) plasmas (ER-CDPs). The velocity autocorrelation function (VACF) and self-diffusion coefficient (*D*) have been investigated through Green-Kubo expressions by using equilibrium MD simulations. The effect of uniaxial electric field (*MT*) on the VACF and *D* of dust particles has been computed along with different combinations of plasma Coulomb coupling (*Γ*) and Debye screening (*κ*) parameters. The new simulation results reflect diffusion motion for lower-intermediate to higher plasma coupling (*Γ*) for the sufficient strength of 0.0 < *M* ≥ *1.5.* The simulation outcomes show that the *MT* significantly affects VACF and *D*. It is observed that the strength of *MT* increases with increasing the *Γ* and up to *κ* = 2. Furthermore, it is found that the increasing trend in *D* for the external applied *MT* significantly depends on the combination of plasma parameters (*Γ*, *κ*)*.* For the lower values of *Γ*, the proposed method works only for the low strength of *MT*; at higher *Γ*, the simulation scheme works for lower to intermediate *MT*, and *D* increased almost 160%. The present results are in fair agreement with parts of other MD data in the literature, with our values generally overpredicting the diffusion motion in ER-CDPs. The investigations show that the present algorithm more effective for the liquids-like and solid-like state of ER-CDPs. Thus, current equilibrium MD techniques can be employed to compute the thermophysical properties and also helps to understand the microscopic mechanism in ER-CDPs.

**Keywords:** Diffusion coefficient, electrorheological complex plasma, Molecular dynamics simulations, uniaxial electric field
