With the rapid development of artificial intelligence and robotics, the application of robotics in the chemical domain is driving a transformation toward intelligent and large-scale research in chemistry and material science. However, sample weighing and synthesis reactions constitute critical stages in chemical experiments, which presents significant challenges for robotic gripping of reagent tubes to achieve precise measurements and collision-free path planning autonomously. Therefore, this study aims to address automation of manipulation in chemical experiments, achieving collision-free path planning and optimization under multi-objective constraints. Specifically, the trajectory planning problem for such tasks is formulated as a multi-objective optimization to minimize motion time, joint jerk and energy consumption. Then, an improved optimized multi-objective particle swarm optimization (OMOPSO) algorithm that incorporates seventh-order polynomial interpolation is proposed to improve the smoothness of robotic motion trajectory. A uniform Pareto front is obtained through a reference vector-guided leader selection mechanism, and an update strategy based on $\epsilon$-domination, and inflection point selection is proposed to balance the convergence and diversity of the solution set. Finally, simulation results and demonstrations on a manipulation platform have fully validated the feasibility and practicality of the proposed method, which further provides a reference for robotic execution of chemical experiments.