# Example: electronic transitions and simulation of electronic emission and absorpton spectra of metal halogenide molecules.

Electronic emission and absorption spectra of BiI and BiCl molecules excited by an electron impact in gas discharge plasma under the conditions of Ar-MeI and Ar-MeCl lighting lamps were simulated. These spectra were recovered on the basis of the present-day knowledge of the potential energy curves involved into the excitation mechanism.

##### Potential energy curves of MeI molecules.

The theoretical modeling of emission and absorption spectra of BiI and BiCl was necessary for modeling gas discharge plasma under the conditions of Ar-MeI and Ar-MeCl lighting lamps. The first stage of modeling performed by the Kintech Lab team consisted in ab initio calculations of the potential energy functions of excited states and transition dipoles of electronic transitions. Kintech Lab experts participated in the development of an appropriate computational technique that allowed the account of large spin-orbit coupling interaction in the excited states of iodine compounds. The curves are presented below.

Left figure - potential energy curves for BiI (solid lines) and BiI- (dashed lines). Red dashed line indicates energy necessary for dissociation. Right figure - potential energy curves for BiCl (solid line) and BiCl- (dashed line) (Kintech Lab, 2005). Red dashed line indicates energy necessary for dissociation.

##### Emission / absorpton spectra simulation

Table 1 contains the parameters of electronic emission and absorption transitions in BiI and BiCl molecules. Te is absorption quantum, ωe is vibrational quantum.

Table 1. Parameters of electronic emission transitions of BiI and BiCl molecules. Vibrational quantum of the ground state: ωe(BiCl/X/)=308.4 cm-1 [2], ωe(BiI/X/)=156 cm-1 [3] (164 cm-1 [2])

Reaction Rates Rates
X = I X = Cl
BiX(a) => BiX + ħω A=1.64•102 1/s, ωe(BiI/a/)=155 1/cm A=1.64•102 1/s
BiX(B[3]0+) => BiX + ħω A=1.0•105 1/s, (lband = 420-435 nm); lmax = 427 nm; dE=2.9 eV; ωe(BiI/B/)=170 1/cm [3] (198 1/cm [2]) A=2.63•105 1/s; (lband = 360-400 nm); lmax = 354 nm; dE=3.15 eV; ωe(BiCl/B/)=403.5 1/cm [2]
BiCl(A[2](0)) => BiCl + ħω   A=1•106 1/s; lmax = 450 nm; dE=2.62 eV

Electron impact excitation. The most intense bands in the emission spectra of these molecules relate to transitions MeI(*) -> MeI(X). These transitions are excited by electron impact:

MeIv(X)  + e -> MeIv’(*) + e  (1)

where v, v’ are vibrational quantum numbers of the lower and upper level, respectively. Within the frame of the Frank-Condon approximation, the magnitudes of the cross section of processes (1) are proportional to the relevant Franc-Condon factors F(v, v’) which were calculated in Kintech Lab.

Vibrational distribution. The populations of vibrational sublevels of the ground state MeIv(X) obey the equilibrium Boltzmann distribution. The magnitude of the vibrational quantum for the molecules under consideration is about 200 – 250 K, while gas temperature is within the range of 500 – 600 K. Therefore, several vibrationally excited states v <5 notably contribute in the excitation processes like (1).

Vibrational relaxation. Electronically and vibrationally excited molecules can decompose as a result of spontaneous radiation

MeIv’(B)  -> MeIv’’(X) + hw    (2)

and collisional vibration relaxation

MeIv’(B)  + Ar -> MeIv’-1 (B)  (3)

The competition between the two decompostion mechanisms determines the molecular emission spectrum. Taking into account vibrational relaxation processes (3) would result in some (about 20%) narrowing of the characteristic width of the molecular emission band.

Rotational distribution. Molecules within a given vibrational distribution are distributed over a manifold of rotational states. This results in the broadening of a specific electron-vibration line. Since the characteristic distance between various individual electron-vibration lines lies between several tens and about one hundred cm-1, some individual transitions can be discriminated against the background of rotational spectrum.

##### BiI and BiCL emission spectra. Calculated and experimental.

Figures below present the emission spectra of BiI and BiCl molecules recovered on the basis of the above-presented approach in their comparison with the experimental data of [3]. The spectra are represented in wavelength scale.

Calculated emission spectra of BiI molecule represented in the wavelength scale.
Experimental emission spectra of BiI molecule [3].
Calculated emission spectra of BiCl molecule represented in the wavelength scale.
Experimental emission spectra of BiCl molecule [3].

##### Conclusions.
• BiI:
• Excellent agreement between the predicted and measured Bi-I molecular signature.
• BiCl:
• Experimental features: A broad continuum from 400-600 nm, peaking from 440-500 nm;
• Calculated features: An intense band from 390-400 nm with weaker broad continuum from 400-470 nm;
• Comparison: Absence of intense bands from 390-400 nm in the experiment and an additional band from 470-600 nm observed experimentally;

The developed approach for the calculation of emission and absorption spectra of diatomic molecules is based on the results of quantum-chemical calculations of electronic potential energy curves. The regular correspondence between the calculated and measured spectra evidences the good predictability of such kind of calculations.

The results of calculations imply a strong dependence of the molecular band width for a bound-bound transition on the mutual arrangement of the ground and excited electronic states of the molecule. In the case when these states are considerably shifted relative to each other, the band width in the emission spectrum can reach very big magnitudes (up to tens percent), as is the case of the SnI molecule. In this case, the spectral intensity of the relevant molecular emission can be very low and poorly discriminated.

##### References.

[1] Huber K.P., Herzhberg G., Molecular spctra and molecular structure, vol.4. Constants of diatomic molecules (Van Nostrand Reinhold, Princetov, 1979).

[2] Alekseyev A.B., Das K.K., Liebermann H.-P., Buenker R.J., Hirsch G., Chem. Phys., 198(1995)333.

[3] Morgan F., Phys. Rev., 49(1936)41