Since complex absorbing potentials (CAPs) are nonphysical in nature, they can introduce artificial perturbations into the system, which may lead to shifts in the calculated energy. This study presents a methodology to eliminate artificial reflections caused by the CAP using a backward parametric equation of motion with the CAP approach (PEMCAP approach), starting from a higher CAP strength parameter $\eta$ to limit of $\eta \to 0^{+}$. During backward PEMCAP approach, the eigenstates as a function of $\eta$ do not follow the same path as the forward trajectory, i.e., starting from $\eta =0$ to higher $\eta$. Instead, the energy converges to the true numerically exact resonance energy, which includes both its position and lifetime. This technique enables us to reach the physical limit $\eta \to 0^{+}$, effectively removing the perturbation caused by the CAP. The effectiveness of this approach is demonstrated by accurate calculations of resonance complex energies that are independent of both the CAP box-size parameters and the optimal value of $\eta$. This makes the optimization of the CAP onset parameters unnecessary. Moreover, this method also allows for the determination of resonance energies corresponding to multiple resonances in the physical limit $\eta \to 0^{+}$ through a single calculation, making this approach extremely beneficial.

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• Scattering of atoms, molecules, clusters & ions