# -*- coding: utf-8 -*- """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! Reference ------------ "Optical Diagnostics and Radiative Emission of Air Plasmas", C. Laux, 1993, p93 Mantz et al 1975, "Ground state molecular constants of 12C16O" """ # %% Dunham development # ... vibrational term (Herzberg notation) def Gv(v, we=0, wexe=0, weye=0, weze=0, weae=0, webe=0, gv=1): """Vibrational energy term Dunham development (order 5 in v) in Herzberg notation. .. math:: 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: float Energy (cm-1) 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 :func:`~radis.phys.morse.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 -------- :py:func:`~radis.levels.dunham.Fv` List of :py:data:`~radis.db.conventions.herzberg_coefficients` Get Herzberg coefficients for a molecule: :py:func:`~radis.db.utils.get_herzberg_coefficients` Use Dunham coefficients instead: :py:func:`~radis.levels.dunham.EvJ` """ return ( we * (v + gv / 2) - wexe * (v + gv / 2) ** 2 + weye * (v + gv / 2) ** 3 + weze * (v + gv / 2) ** 4 + weae * (v + gv / 2) ** 5 + webe * (v + gv / 2) ** 6 ) # + .. # : : # : : # In Mantz and Maillard 1975 - weze*(v+gv/2)**4 # Mantz 1975 - webe*(v+gv/2)**6 # ... rotational term (Herzberg notation) def 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, ): """Rotational energy term Dunham development (order 4 in J) in Herzberg notation. .. math:: 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) *generated from the Python formula with* :py:func:`~pytexit.pytexit.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: float Energy (cm-1) 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 -------- :py:func:`~radis.levels.dunham.Gv` List of :py:data:`~radis.db.conventions.herzberg_coefficients` Get Herzberg coefficients for a molecule: :py:func:`~radis.db.utils.get_herzberg_coefficients` Use Dunham coefficients instead: :py:func:`~radis.levels.dunham.EvJ` """ B_e, D_e, H_e, g_v = Be, De, He, gv # ... Note: formula added in docstring with pytexit.py2tex() # + ... B_v = ( B_e - alpha_e * (v + g_v / 2) + gamma_e * (v + g_v / 2) ** 2 + delta_e * (v + g_v / 2) ** 3 + epsilon_e * (v + g_v / 2) ** 4 ) D_v = D_e + beta_e * (v + g_v / 2) + pi_e * (v + g_v / 2) ** 2 # + ... H_v = H_e - eta_e * (v + g_v / 2) # : : # : : # In Mantz and Maillard 1975 - delta_e*(v+gv/2)**3 # - beta_e*(v+gv/2) in Mantz and Maillard 1975 return B_v * J * (J + 1) - D_v * (J * (J + 1)) ** 2 + H_v * (J * (J + 1)) ** 3 # ... general term # def EvJ(v, J, **Ykl_dict): # ''' Calculates rovibrational energy reading from Dunham coefficients in # Ykl notation # # Parameters # ---------- # # Ykl: dict # an arbitrary dictionary of Ykl coefficients # accepted formats: Y01, Y01_cm-1 # # Ykl are parsed and assigned the correct energy # # Notes # ----- # # Because reading and parsing the Ykl dict is required, this is expected to # be slower that a hardcoded implementation. However, it is also much # more flexible. # # # 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) # # ''' # # E = 0 # # Ykl_format = '^Y(?P[0-9])(?P[0-9])(_cm-1)?$' # # ... Ykl with k, l ints and followed by nothing or _cm-1 # # ... accepted formats: Y01, Y01_cm-1 # reg = re.compile(Ykl_format) # # for ykl_name, Ykl in Ykl_dict.items(): # match = reg.search(ykl_name) # if match is None: # raise ValueError(f'Key {ykl_name} does not have the expected format {Ykl_format}') # res = match.groupdict() # k = int(res['k']) # l = int(res['l']) # E += Ykl * (v+0.5)**k * (J*(J+1))**l # # return E # New version (less versatile, but less Python and faster) # only allowed formats: Y01 def EvJ(v, J, **Ykl_dict): """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 Dunham coefficients for a molecule: :py:func:`~radis.db.utils.get_dunham_coefficients` Use Herzberg coefficients instead: :py:func:`~radis.levels.dunham.Gv`, :py:func:`~radis.levels.dunham.Fv` """ E = 0 for ykl_name, Ykl in Ykl_dict.items(): k = int(ykl_name[1]) l = int(ykl_name[2]) E += Ykl * (v + 0.5) ** k * (J * (J + 1)) ** l return E if __name__ == "__main__": from radis.test.phys.test_dunham import _run_all_tests print("Testing Dunham.py: ", _run_all_tests())