Molecule Types Linear Molecules <Prev Next>

Linear Molecule State

This contains the rotational constants and other information specific to each state within a linear molecule. Note that PGOPHER will calculate Hund's cases (a) and (b) exactly. Other cases can be handled, but typically require more work to set up. For Hund's case (c), for example it may make sense to treat the various components of a state separately, which is possible by setting up multiple copies of the state and making use of the OmegaSelect and/or ParitySelect settings. For example the two halves of a 2Π state can be treated separately by setting up two 2Π states, one with OmegaSelect = ½ and one with OmegaSelect = 3/2.

Settings

Colour Colour - set to "None" to take value from elsewhere as explained in Determining Colours and J ranges.
RveSelect Only include given rovibronic symmetry - for normal use set to 'all'
S Electron Spin
Lambda Electronic angular momentum - use Sigma-, Sigma+, Pi, Delta, Phi, Gamma, H, I or a numerical value
gerade True for gerade (g) states, false for ungerade (u) states; ignored if the molecule is not symmetric as specified by the Symmetric setting for the molecule.
OmegaSelect Set to all for normal use; set to a specific value to restrict the basis states to a specific value of Ω. Basis states with other values of Ω are deleted, which will typically change calculated energies. (If you just want to display selected transitions, use the transitions window.) Note that if OmegaSelect is used the F1/F2/F3 numbering and N assignment may not be consistent, particularly for versions before 8.0.326. This is because of the algorithm used to determine if the state is regular or inverted; the OmegaOrder setting below can be used to force the desired  order.
OmegaOrder This is only used in assigning N, Ω and F1/F2/F3... quantum numbers to final states, and the default (Auto) is sufficient for all but rather unusual calculations. Possible values are Auto (the default), Regular (implying energies are expected to increase with Ω) and Inverted (energies decrease with Ω). The algorithm for assigning quantum numbers assumes energies increase with N and F number, so this controls how Ω is matched to these. In addition, if LimitSearch is set (the default), the expected energy ordering is used to assign the N and F1/F2/F3... quantum numbers.

Parameters

Origin State Origin.
Width Linewidth (rotation independent) for state.
B Rotational constant. Rotation
A Spin-orbit coupling constant. Spin-Orbit
LambdaSS Spin - spin coupling constant, λ (=1.5*ε). Spin-Spin
o Spin-spin coupling constant giving lambda doubling for Omega = 0 states. Λ Doubling
theta Higher Order Spin-Spin interaction (S>=2 only). Spin-Spin
Gamma Spin rotation coupling constant. Spin-Rotation
p Lambda doubling constant. Λ Doubling
q Lambda doubling constant. Λ Doubling
D Quartic centrifugal distortion. Rotation
H Sextic centrifugal distortion. Rotation
L J8 centrifugal distortion. Rotation
M J10 centrifugal distortion. Rotation
PP J12 centrifugal distortion. (Not P to avoid confusion with p.) Rotation
LambdaD Centrifugal Distortion of λ. Spin-Spin
LambdaH J4 Centrifugal Distortion of λ. Spin-Spin
oD Centrifugal distortion of o for Π states. n for Δ states.
Λ Doubling
oH J4 Centrifugal distortion of o for Π states. o for Δ states. Λ Doubling
oL J6 Centrifugal distortion of o for Π states only. Λ Doubling
pD Centrifugal distortion of p for Π states only. Λ Doubling
pH J6 Centrifugal distortion of p for Π states only. Λ Doubling
pL J8 Centrifugal distortion of p for Π states only. Λ Doubling
qD Centrifugal distortion of q for Π states only. Λ Doubling
qH J6 Centrifugal distortion of q for Π states only. Λ Doubling
qL J8 Centrifugal distortion of q for Π states only. Λ Doubling
gammaD Centrifugal distortion of gamma. Spin-Rotation
gammaH J6 Centrifugal distortion of gamma. Spin-Rotation
gammaL J8 Centrifugal distortion of gamma. Spin-Rotation
eta Additional spin orbit term for quartet and higher states Spin-Orbit
gammaS Additional spin rotation term for quartet and higher states Spin-Orbit
AD Centrifugal distortion of A. Spin-Orbit
AH J2 Centrifugal distortion of A. Spin-Orbit
AL J4 Centrifugal distortion of A. Spin-Orbit
AM J6 Centrifugal distortion of A. Spin-Orbit
Note that the lambda doubling is only implemented fully for Π states. A partial implementation is available for Δ states - see  Λ type doubling for Δ and higher states, and any required terms can be added using perturbations.