Created on Tue Jul 18 17:47:48 2017.

@author: erwan

Dunham development for diatomic molecules energies

Warning

Although by convention prefactors share the same name throughout most of the litterature, signs can be different depending on the article. Make sure your Dunham expansion has the same signs as the one we use here!

“Optical Diagnostics and Radiative Emission of Air Plasmas”, C. Laux, 1993, p93 Mantz et al 1975, “Ground state molecular constants of 12C16O”

EvJ(v, J, **Ykl_dict)[source]

Calculates rovibrational energy reading from Dunham coefficients in Ykl notation, for diatomic molecules.

Parameters
• Ykl (dict) – an arbitrary dictionary of Ykl coefficients accepted formats: Y01

• Ykl are parsed and assigned the correct energy

Examples

Read directly from a .json file:

from radis.db.utils import get_dunham_coefficients
from radis.levels.dunham import EvJ
dunham_coeffs = get_dunham_coefficients('CO', 1, 'X1SIG+')

# Now calculate energy
EvJ(v=0, J=0, **dunham_coeffs)


Get, Use, Fv()

Fv(v, J, Be=0, De=0, alpha_e=0, beta_e=0, gamma_e=0, delta_e=0, epsilon_e=0, pi_e=0, He=0, eta_e=0, gv=1)[source]

Rotational energy term Dunham development (order 4 in J) in Herzberg notation.

\begin{align}\begin{aligned}B_{v}=B_{e}-\alpha_{e}\left(v+\frac{g_{v}}{2}\right)+\gamma_{e} \left(v+\frac{g_{v}}{2}\right)^{2}+\delta_{e}\left(v+\frac{g_{v}}{2} \right)^{3}+\epsilon_{e}\left(v+\frac{g_{v}}{2}\right)^{4}\\D_{v}=D_{e}+\beta_{e}\left(v+\frac{g_{v}}{2}\right)+\pi_{e} \left(v+\frac{g_{v}}{2}\right)^{2}\\H_{v}=H_{e}-\eta_{e}\left(v+\frac{g_{v}}{2}\right)\end{aligned}\end{align}

generated from the Python formula with py2tex()

Parameters
• v (int) – vibrational quantum number

• J (int) – rotational quantum number

• Be (float) – rotational constant in equilibrium position (cm-1)

• De (float) – centrifugal distortion constant (cm-1)

• alpha_e (float) – rotational constant – first term (cm-1)

• beta_e (float) – rotational constant – first term, centrifugal force (cm-1)

• gamma_e (float) – rotation-vibration interaction constant (cm-1)

• delta_e (float) – (cm-1)

• epsilon_e (float) – (cm-1)

• pi_e (float) – (cm-1)

• He (float) – third order correction factor (cm-1)

• eta_e (float) – (float)

• gv (int) – degeneracy (usually 1, but 2 for CO2-v2)

Returns

Fv – Energy (cm-1)

Return type

float

Notes

Validity:

For large vibrational levels Dunham’s expansion is not valid. In RADIS a Morse Potential can be used above a certain vibrational level

Warning

Although by convention prefactors share the same name throughout most of the litterature, signs can be different depending on the article. Make sure your Dunham expansion has the same signs as the one we use here! Ex:

• Mantz and Maillard 1975 (CO) uses opposite signs for delta_e and beta_e

References

“Optical Diagnostics and Radiative Emission of Air Plasmas”, C. Laux, 1993, p93

Gv(), List, Get, Use

Gv(v, we=0, wexe=0, weye=0, weze=0, weae=0, webe=0, gv=1)[source]

Vibrational energy term Dunham development (order 5 in v) in Herzberg notation.

$G_v = w_e\left(v+\frac{g_v}{2}\right) - w_ex_e\left(v+\frac{g_v}{2}\right)^2 + w_ey_e\left(v+\frac{g_v}{2}\right)^3 + w_ez_e\left(v+\frac{g_v}{2}\right)^4 + w_ea_e\left(v+\frac{g_v}{2}\right)^5$
Parameters
• v (int) – vibrational quantum number

• we (float) – vibrational constant – first term (cm-1)

• ωexe (float) – vibrational constant – second term (cm-1)

• ωeye (float) – vibrational constant – third term (cm-1)

• ωeze (float) – vibrational constant – fourth term (cm-1)

• weae (float) – vibrational constant – fifth term (cm-1)

• webe – vibrational constant – sixth term (cm-1)

• gv (int) – degeneracy (usually 1, but 2 for CO2-v2)

Returns

Gv – Energy (cm-1)

Return type

float

Notes

Validity:

For large vibrational levels Dunham’s expansion is not valid. In other LBL codes, such as Specair, Morse Potential is used above a certain vibrational level. See morse_increment() for an implementation in RADIS.

Warning

Although by convention prefactors share the same name throughout most of the litterature, signs can be different depending on the article. Make sure your Dunham expansion has the same signs as the one we use here! In particular, this function uses a -wexe sign as in the usual Herzberg notation. Ex:

• Mantz and Maillard 1975 (CO X) uses opposite signs for weze and webe

References

“Optical Diagnostics and Radiative Emission of Air Plasmas”, C. Laux, 1993, p93

Fv(), List, Get, Use