Frenkel line in a dipolar fluid: decoupling of sound dispersion and transverse waves

The Frenkel line, which marks the crossover from gas-like to solid-like dynamics in fluids, has been extensively studied in simple and molecular systems but remains unexplored for dipolar fluids. Using molecular dynamics simulations of a model diatomic dipolar fluid (parametrized after CO), we locate the Frenkel line along the supercritical isotherm $T=800$ K using two criteria: the isochoric heat capacity cV/kB = 3.0 and the disappearance of oscillations in the velocity autocorrelation function. Both criteria consistently place the Frenkel line at a density of ρ ≈ 1.1 g/ml. Analysis of the excitation spectra reveals an unusual decoupling: positive sound dispersion already appears at ρ=0.9 g/ml, whereas transverse (shear) waves emerge only at the Frenkel line density of ρ=1.1 g/ml. The magnitude of the positive sound dispersion is about $20 %$, similar to that in simple monatomic melts. For the first time, we investigate rotational dynamics across the Frenkel line using the autocorrelation functions C₁(t) and C₂(t). The corresponding correlation times τ₁ and τ₂ increase monotonically with density and show no detectable anomaly upon crossing the Frenkel line. Our results suggest that although translational dynamics exhibit a clear crossover at the Frenkel line, rotational motion in dipolar fluids is not significantly affected.