Interpretation and analysis of perturbed spectra of axially symmetric molecules with applications to ¹³CD₃F

The main thrust of this study is the development and testing of an algorithm to fit perturbed vibration-rotation molecular spectra. The algorithm is first developed in a general form and then applied to the vibration-rotation spectra of axially symmetric molecules using simulated data.

13 The 5 µm absorption spectrum of ¹³CD₃F is very complex. There are 24 vibrational levels in the region from 1800 cm^-1 to 2250 cm^-1. There are many strong vibrational and rotational resonances linking these states. The states included in this analysis are ν₄(ℓ₄=±1), 2ν₂(ℓ=0), ν₂+&nu₅(ℓ₅=±1), 2ν₅(ℓ₅=0,±2), &nu₂+&nu₃(ℓ = 0), ν₁(ℓ = 0), and ν₃+ν₅(ℓ₅=±1), all of which lie above 2050 cm^-1. The states omitted in this analysis are ν₂+ν₆(ℓ₆=±1), ν₅+ν₆(ℓ₅=±1, ℓ₆=±1), 2ν₃(ℓ=0), ν₅+ν₆(ℓ₅=±1, ℓ₆=±1), 2ν₆(ℓ₆=0, ±2), all of which lie below 2025 cm ^-1. These two groups of vibrational states are weakly linked by a higher order vibration-rotation resonance between ν₁ and ν₂ +ν₆(ℓ₆=-1), and a weak vibrational resonance between ν₁ and 2ν₃.

The absorption spectrum of ¹³CD₃F was recorded at a resolution of 0.018 cm^-1 and deconvolved to an effective resolution of 0.006 cm^-1. The ν₁, 2ν₅(ℓ₅=0), 2ν₂ and ν₄(ℓ₄=±1) bands were analyzed individually to obtain estimates of the molecular parameters of these states. The local and nonlocal resonances were characterized and interaction constants were estimated which gave a qualitative agreement with the observed spectrum.

The parameters were then refined using a Hamiltonian model which included all possible interactions from the vibration-rotation Hamiltonian through third order with the restriction that ΔΚ-∑Δℓ=0.