The transition rules for pure rotational spectra dictate which changes in rotational energy levels are allowed when a molecule absorbs or emits a photon.
Pure rotational spectra typically occur in the microwave region of the electromagnetic spectrum and involve transitions between different rotational energy levels within the same vibrational and electronic state. For a molecule to exhibit a pure rotational spectrum, it must possess a permanent electric dipole moment.
Rotational Transition Selection Rules
The fundamental rules governing pure rotational transitions are known as selection rules. These rules arise from the conservation of angular momentum and the interaction of the molecule's dipole moment with the electric field of the photon. The specific selection rules depend on the electronic state of the molecule, specifically the value of the component of the electronic angular momentum along the internuclear axis, denoted by Λ.
Based on spectroscopic principles and the provided reference, the selection rules for changes in the total angular momentum quantum number, J, are:
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When Λ = 0: For molecules in electronic states where the component of the total electronic angular momentum along the internuclear axis (Λ) is zero (e.g., Σ electronic states in diatomic molecules), the selection rule for the total angular momentum quantum number (J) is strictly ΔJ = ±1.
- ΔJ = +1: Corresponds to the absorption of a photon, leading to a transition to a higher rotational energy level.
- ΔJ = -1: Corresponds to the emission of a photon, leading to a transition to a lower rotational energy level.
Example: A molecule in a Σ state can undergo transitions from J=0 to J=1, J=1 to J=2, etc., upon absorption, or J=1 to J=0, J=2 to J=1, etc., upon emission.
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When Λ ≠ 0: For molecules in electronic states where the component of the total electronic angular momentum along the internuclear axis (Λ) is not zero (e.g., Π or Δ electronic states in diatomic molecules), the selection rule for the total angular momentum quantum number (J) is ΔJ = 0, ±1.
- ΔJ = +1: Absorption transition to a higher J level.
- ΔJ = -1: Emission transition to a lower J level.
- ΔJ = 0: While a change in J is usually required for a pure rotational transition to absorb or emit a photon, the Λ ≠ 0 case allows for ΔJ=0 transitions due to interactions between the electronic angular momentum and the overall rotation (such as Λ-doubling). As the reference states, "absorbed or emitted photon can make equal and opposite change in total nuclear angular momentum and total electronic angular momentum without changing value of J." This means the photon's angular momentum can be absorbed by the electronic angular momentum while the rotational angular momentum remains unchanged, leading to a spectroscopic transition (e.g., between Λ-doublet components).
Example: A molecule in a Π state could potentially transition from J=1 to J=2 (ΔJ=+1), J=2 to J=1 (ΔJ=-1), or even undergo a transition between different components of a split level at the same J (ΔJ=0).
Summary of Selection Rules for J
| Electronic State | Component of Electronic Angular Momentum (Λ) | Allowed Change in Total Angular Momentum (ΔJ) |
|---|---|---|
| Σ | Λ = 0 | ±1 |
| Π, Δ, etc. | Λ ≠ 0 | 0, ±1 |
These selection rules, particularly ΔJ = ±1 for Λ=0 states, are fundamental to understanding the structure of pure rotational spectra, which appear as a series of lines typically spaced by approximately 2B, where B is the rotational constant of the molecule.
