In addition, ergodicity in the configurational space is critical for the convergence of the simulated macrostate properties. Enhanced sampling methods, such as umbrella sampling (US), adaptively biased molecular dynamics (ABMD), and metadynamics, are now frequently employed to boost one or two DoF and thereby accelerate the reaction. For the orthogonal DoF, the exploration can still be hindered by hidden barriers, and a ns-timescale simulation can be inevitable. Besides, length of the simulations determines the effective number of samples, because independent and identically distributed (i.i.d.) samples are required for the calculations of ensemble averages. For simulations in aqueous solutions, the energy correlation time is on a scale around 1 ps. If the samples are saved too frequently, sampling inefficiency must be considered. Affordable studies are limited to relatively simple systems, 42 low levels of theory, or with the aid of artificial intelligence. Therefore, it is desirable to develop a practical method for the study of thermodynamics properties based on PIMD that can dramatically reduce the computational expense while maintain the accuracy. The multistate thermodynamic perturbation (MsTP) is the method of choice, of which the efficiency and reliability has been examined by Li et al. in an early study of some model reactions. MsTP is a variant of the reference-potential method, in which the ensemble averages of any time-independent physical properties at a high level of theory are obtained indirectly from simulations at a lower level of theory. With further improvement, this method is becoming more robust for the studies of chemical processes in the condensed phase.