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See Making a linear molecule data file and the worked example: The Schumann-Runge Bands of O2 for an introduction to working with linear molecules.
PGOPHER will calculate Hund's cases (a) and (b) exactly, and will work with the other possible cases, though these typically require more work to set up.
J |
Total angular momentum excluding
nuclear spin |
F |
Total angular momentum |
S |
Total electron spin angular momentum. This must be set for each State |
N |
J-S = Total angular momentum excluding nuclear and electron spin. |
Λ | The projection of the electronic orbital angular momentum onto the z axis of the molecule. This must be set for each State |
Ω | The projection of J onto the axis of the molecule; Ω
= Λ + Σ where Σ is the projection of S
onto the axis of the molecule. |
Fn |
The notation F1, F2,
F3 ... is an alternative notation for the
components of a multiplet, ordered by energy with with F1
being the lowest. |
|Name J +- Omega>where Name is the manifold and state name. If hyperfine structure is included in the calculation then F (and intermediate quantum numbers if there is more than one nucleus) is added to the end.
Name |
The manifold and state name |
J |
The J quantum number; not shown if ShowJ is false at the Molecule level |
N |
The N quantum number; not shown if ShowN is false at the Molecule level or all states are singlet states |
Ω | The Ω quantum number; not shown if ShowOmega is false at the Molecule level (the default) or all states are singlet states |
Fn |
The component of the multiplet
numbered from 1 in order of increasing energy; not shown if ShowFNumber is false at the Molecule level or all states are singlet
states. This contains the same information as the Ω quantum number, so
it does not usually make sense to show both. |
e/f |
The parity; not shown if Showef is false at the Molecule level. |
Hyperfine quantum numbers are
added at the end as required. |
X v=0 7.5 7 F1e
Note that the only guaranteed quantum numbers are the total angular momentum and symmetry; while PGOPHER tries to work out sensible assignments of the other quantum numbers there are cases where this is not possible, or the choice the program makes is not the same as other programs. This most commonly arises in the case of perturbations, or where S > J. The algorithm used can be adjusted by the EigenSearch and LimitSearch settings at the Manifold level; you may want to use LimitSearch = True as this can give more consistent results for the F1/F2... labels. Variations in the quantum number assignment does not affect other parts of the calculation, so the simulated positions and intensities are not affected by these considerations.