The appearance of a second excitation mode in the longitudinal and transverse collective dynamics
of a series of liquid metals has been observed recently, either by inelastic X-ray scattering (IXS) or
by first-principles molecular dynamics (FPMD). The phenomenon’s origin is still uncertain, although
some theories have been used with relative success to reproduce the FPMD results as a means to
find an explanation for it (e.g., mode-coupling (MC) theory in liquid zinc [B. G. del Rio and L. E.
González, Phys. Rev. B 95, 224201 (2017)]). For liquid tin (l-Sn), the second excitation mode in the
dynamic structure factor and longitudinal current spectrum was observed by IXS [S. Hosokawa et al.,
J. Phys.: Condens. Matter 25, 112101 (2013)]. By performing orbital-free density functional theory
MD simulations of l-Sn, we confirm the existence of a second excitation mode in the longitudinal and
transverse collective dynamics and provide a theoretical explanation based on MC theory. Moreover,
we introduce a new binary term in MC theory to better capture the negative minima present in the
memory functions of the collective dynamics. These results confirm that the origin of the second
excitation mode exhibited by the longitudinal and transverse collective dynamics in some liquid
metals involves an indirect coupling of the longitudinal and transverse modes.
