Suppose that three conformations are proposed for the nonlinear molecule H₂O₂ (1, 2, and 3). The infrared absorption spectrum of gaseous H₂O₂ has bands at 870, 1370, 2869, and 3417 cm⁻¹. The Raman spectrum of the same sample has bands at 877, 1408, 1435, and 3407 cm⁻¹. All bands correspond to fundamental vibrational wavenumbers and you may assume that:

(a) The 870 and 877 cm⁻¹ bands arise from the same normal mode, 

(b) The 3417 and 3407 cm⁻¹ bands arise from the same normal mode.

(i) If H₂O₂ were linear, how many normal modes of vibration would it have?

(ii) Give the symmetry point group of each of the three proposed conformations of nonlinear H₂O₂.

(iii) Determine which of the proposed conformations is inconsistent with the spectroscopic data. Explain your reasoning.

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