  F\"orster resonance energy transfer (FRET) is a quantum mechanical phenomenon
involving the non-radiative transfer of energy between coupled electric
dipoles. Due to the strong dependence of FRET on the distance between the
dipoles, it is frequently used as a ``molecular ruler" in biology, chemistry,
and physics. This is done by placing dipolar molecules called dyes on molecules
of interest. In time-resolved confocal single-molecule FRET (smFRET)
experiments, the joint distribution of the FRET efficiency and the donor
fluorescence lifetime can reveal underlying molecular conformational dynamics
via deviation from their theoretical F\"orster relationship. This deviation is
referred to as a dynamic shift. Quantifying the dynamic shift caused by the
motion of the fluorescent dyes is essential to decoupling the dynamics of the
studied molecules and the dyes. We develop novel Langevin models for the dye
linker dynamics, including rotational dynamics, based on first physics
principles and proper dye linker chemistry to match accessible volumes
predicted by molecular dynamics simulations. By simulating the dyes' stochastic
translational and rotational dynamics, we show that the observed dynamic shift
can largely be attributed to the mutual orientational dynamics of the electric
dipole moments associated with the dyes, not their accessible volume.
