Fig. 1. The IR spectra for HCHO at both 300 K and 100 K. Purple dotted lines represent exact frequencies.

Fig. 2. The IR spectra for isotope molecules of HCHO for 300 K. Purple dotted lines represent exact frequencies.

Fig. 3. The IR spectra for H₂O₂ at both 300 K and 100 K. Purple dotted lines represent exact frequencies.

Fig. 4. The IR spectra for isotope molecules of H₂O₂ for 300 K. Purple dotted lines represent exact frequencies.

Table 1. Peak positions of the HCHO molecule at different temperatures. PES and exact results from Ref.[37] (unit: cm⁻¹).

Table 2. Peak positions of isotope molecules of the HCHO molecule at 300 K. PES and exact results from Ref.[37] (unit: cm⁻¹).

Table 3. Corresponding peak position red-shifts of the isotope molecules to the HCHO molecule at 300 K. Calculated based on Table Ⅰ and Table Ⅱ (unit: cm⁻¹):

Table 4. Peak positions of the H₂O₂ molecule at different temperatures. PES and exact results from Refs.[38, 45] (unit: cm⁻¹). Tunneling splitting values for the PES are available in Ref.[45]. NMA captures no tunneling splitting effects. Experimental results are listed for comparison.

Table 5. Peak positions of isotope molecules of the H₂O₂ molecule at 300 K. PES and exact results from Refs.[38, 45] (unit: cm⁻¹). The tunneling splitting value is available only for the first fundamental of H₂¹⁸O₂, HDO₂, or D₂O₂ in Ref.[45]. NMA captures no tunneling splitting effects.

Table 6. Corresponding peak position red-shifts of the D₂O₂ molecule from the H₂O₂ molecule at 300 K. Calculated based on Table Ⅳ and Table Ⅴ (unit: cm⁻¹). Except for the first fundamental corresponding to the torsion mode, the exact red-shift value is obtained by using the average of the two tunneling splitting peak positions of the fundamental of the H₂O₂ molecule as the reference.