radis.levels.dunham module¶
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 literature, 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)
See also
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 literature, 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
See also
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 literature, 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
See also
Fv()
,List
,Get
,Use