  Quantum-classical molecular dynamics, as a partial classical limit of the
full quantum Schr\"odinger equation, is a widely used framework for quantum
molecular dynamics. The underlying equations are nonlinear in nature,
containing a quantum part (represents the electrons) and a classical part
(stands for the nuclei). An accurate simulation of the wave function typically
requires a time step comparable to the rescaled Planck constant $h$, resulting
in a formidable cost when $h\ll 1$. We prove an additive observable error bound
of Schwartz observables for the proposed time-splitting schemes based on
semiclassical analysis, which decreases as $h$ becomes smaller. Furthermore, we
establish a uniform-in-$h$ observable error bound, which allows an
$\mathcal{O}(1)$ time step to accurately capture the physical observable
regardless of the size of $h$. Numerical results verify our estimates.
