NBS Monograph 115 -
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The Calculation of Rotational Energy Levels
and Rotational Line Intensities in Diatomic Molecules
Jon T. Hougen
Gloria Wiersma, HTML conversion
Procedures are described, in this pedagogical monograph, for making quantum
mechanical calculations of rotational energy levels and rotational line
intensities in diatomic molecules. The procedures are illustrated by sample
calculations. A familiarity with the material of this report should enable a
practicing electronic spectroscopist to carry out, though in a rather
mechanical way, his own theoretical calculations for molecules under
experimental investigation. The material of this report is aimed at electronic
spectroscopists who have had the equivalent of one semester of graduate level
quantum mechanics.
Key words: Diatomic molecules; Hund's coupling cases; rotational levels;
rotational line intensities; theoretical calculations.
Table of Contents - Cover Page
1970 document
- Preface
- 1. Calculation of rotational energy levels
- 1.1. Hund's coupling cases (a), (b), (c), and (d)
- 1.2. General approach to the calculations
- 1.3. Nonrotating-molecule Hamiltonian
- 1.4. Nonrotating-molecule basis set
- 1.5. Nonrotating-molecule matrix elements
- 1.6. Rotating-molecule Hamiltonian
- 1.7. Rotating-molecule basis set
- 1.8. Rotating-molecule matrix elements
- 1.9. Example: The Hill and Van Vleck expression
for 2Π states
- 1.10. Example: The Schlapp expression for
3Σ States
- 2. Symmetry properties of the rotational energy
levels
- 2.1. Geometric symmetry operations
- 2.2. Permutation-inversion symmetry operations
- 2.3. The symmetry operation
σv
- 2.4. Example: Parities of the rotational levels in a
1Σ- state
- 2.5. Example: Parities of the rotational
levels in a 3Σ+ state
- 2.6. The symmetry operation i
- 2.7. The symmetry operation
C2
- 2.8. Example: Symmetry properties of the
rotational levels in a 1Πu state
- 2.9. Relations between matrix elements
- 2.10. Example:
≡ L2 -
Lz2
- 2.11. The time inversion operation θ
- 3. Calculation of rotational line intensities
- 3.1. Laboratory-fixed components of the electric
dipole moment operator ยต
- 3.2. Molecule-fixed components of µ
- 3.3. The direction cosine matrix α
- 3.4. Example: Hönl-London intensity
expressions for a 1Π -
1Σ+ transition
- 3.5. Example: Rotational intensity distribution in
a 3Σ-
- 1Σ+ transition
- 3.6. Intensity calculations when closed-form
expressions cannot be obtained.
Example: Rotational intensity distribution
in a 4Δ - 6Σ+
transition
- 4. Perturbations
- 4.1. General remarks
- 4.2. Homogeneous and heterogeneous perturbations
- 4.3. Example:
1Π - 1Σ+
heterogeneous perturbation
- 4.4. Example:
3Δ - 1Π homogeneous
perturbation
- 4.5. Van Vleck transformations
- 4.6. Example: Λ-type doubling
in a 1Π state
- 4.7. Centrifugal distortion corrections to rotational energy levels
- 5. References
- Footnotes
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Online: June 2001 - Last update: July 2007
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