Accurate and efficient integration of the equations of motion is indispensable for molecular dynam-ics (MD) simulations.Despite the massive use of the conventional leapfrog (LF) integrator in mod-ern computational tools within the framework of MD propagation,further development for better performance is still possible.The alternative ver-sion of LF in the middle thermostat scheme (LF-middle) achieves a higher order of accuracy and ef-ficiency and maintains stable dynamics even with the integration time stepsize extended by several folds.In this work,we perform a benchmark test of the two integrators (LF and LF-middle) in ex-tensive conventional and enhanced sampling sim-ulations,aiming at quantifying the time-stepsize-induced variations of global properties (e.g.,de-tailed potential energy terms) as well as of local observables (e.g.,free energy changes or bond-lengths) in practical simulations of complex sys-tems.The test set is composed of six chemically and biologically relevant systems,including the conformational change of dihedral flipping in the N-methylacetamide and an AT (Adenine-Thymine) tract,the intra-molecular proton transfer inside malonaldehyde,the binding free energy calculations of benzene and phenol targeting T4 lysozyme L99A,the hydroxyl bond variations in ethaline deep eutectic solvent,and the potential energy of the blue-light using flavin photoreceptor.It is observed that the time-step-induced error is smaller for the LF-middle scheme.The outperformance of LF-middle over the conventional LF integrator is much more significant for global properties than local observables.Overall,the current work demonstrates that the LF-middle scheme should be preferably applied to obtain accurate thermodynamics in the simulation of practical chemical and biological systems.