Decoding Pure Rotational Molecular Spectra for Asymmetric Molecules

Table 1

Summary of transition patterns and features.

Transition type	Frequency	Notes
𝑅−branch, 𝐽^′=𝐽^′′+1
𝑎-type
	(𝐵+𝐶)(𝐽^′′+1)	For each, 𝐽^′←𝐽^′′, with 𝐽^′′>0, transitions are spread over (𝐵−𝐶)(𝐽^′′+1)
𝑏-type
𝐽^′1,𝐽′←𝐽^′′0,𝐽′′	𝐴+𝐶+2𝐶𝐽^′′
𝐽^′0,𝐽′←𝐽^′′1,𝐽′′	(3𝐵+2𝐶−𝐴)+2𝐵(𝐽^′′−1)
𝐽^′2,𝐽′−1←𝐽^′′1,𝐽′′−1	(3𝐴+𝐶+(𝐵−𝐶)/2)+(𝐵+𝐶)(𝐽^′′−1)	Doublet split by ((𝐵−𝐶)/2)𝐽^′𝐽^′′
𝐽^′2,𝐽′−2←𝐽^′′1,𝐽′′
𝐽^′3,𝐽′−2←𝐽^′′2,𝐽′′−2; 𝐽^′3,𝐽′−3←𝐽^′′2,𝐽′′−1	(5𝐴+𝐶+(𝐵−𝐶)/2)+(𝐵+𝐶)(𝐽^′′−2)	Very closely spaced doublets
𝑐-type
𝐽^′1,𝐽′−1←𝐽^′′0,𝐽′′	𝐴+𝐵+2𝐵𝐽^′′
𝑄-branch, 𝐽^′=𝐽^′′
𝑎-type
𝐽1,𝐽−1←𝐽1,𝐽	J = 2: 𝜈=3(𝐵−𝐶)	J = 2: 𝜈(𝐽)=𝑣(𝐽−1)+(𝐵−𝐶)𝐽
𝐽𝐽,1←𝐽𝐽−2,2	2(𝐴−2(𝐵+𝐶))(𝐽−1)	Groups of same 𝐾−1
𝑏-type
𝐽2,𝐽−2←𝐽1,𝐽−1	J = 2: 𝜈=3(𝐴−𝐵)	J > 2: 𝜈(𝐽)=𝜈(𝐽−1)−((𝐵−𝐶)/2)𝐽
𝐽2,𝐽−1←𝐽1,𝐽	J = 2: 𝜈=3(𝐴−𝐶)	J > 2: 𝜈(𝐽)=𝜈(𝐽−1)+((𝐵−𝐶)/2)𝐽