Spectroscopic study of the 24Mg35Cl and 24Mg37Cl A²pi-X²sigma+ band system

Abstract

The A²pi-X²sigma+ emission band system of the MgCl molecule has been studied by means of high resolution Fourier Transform Spectroscopy (FTS). The MgCl species were produced by mixing Mg vapor with a gaseous flow of a He/Cl2 and excited in a ''heated'' Schüller's type discharge tube. Rovibrational analysis of the 0-0 and 0-1 bands was performed and the values of the vibrational constant <FONT FACE=Symbol>we</FONT> of the ground state and the spin-orbit constants A0 and A J of the A2pi state were determined. For the first time transitions of the isotopic species 24Mg37Cl could be assigned and included in the analysis presented here.

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Spectroscopic study of the ²⁴Mg³⁵Cl and ²⁴Mg³⁷Cl A²P-X²S⁺ band system

R. F. Gutterres; Roberto Ferreira dos Santos; C. E. Fellows

Laboratório de Espectroscopia e Laser, Instituto de Física, Universidade Federal Fluminense, Campus da Boa Viagem, Niterói, RJ 24210-340, Brazil

ABSTRACT

The A²P-X²S⁺ emission band system of the MgCl molecule has been studied by means of high resolution Fourier Transform Spectroscopy (FTS). The MgCl species were produced by mixing Mg vapor with a gaseous flow of a He/Cl₂ and excited in a ''heated'' Schüller's type discharge tube. Rovibrational analysis of the 0-0 and 0-1 bands was performed and the values of the vibrational constant !e of the ground state and the spin-orbit constants A₀ and A_J of the A₂P state were determined. For the first time transitions of the isotopic species ²⁴Mg³⁷Cl could be assigned and included in the analysis presented here.

1 Introduction

Alkaline-earth mono-halides molecules are highly ionic compounds and have nine valence electrons outside closed shells. This particular electronic configuration have attracted the interest of theoretical and experimental spectroscopists. Several ionic bonding models have been developed to represent the electronic structure of these first excited states [1-3] and experimental studies of these molecules have allowed the test of these models.

The electronic transitions involving the ground and the first excited states of the MgCl molecule have been studied [4-13] from different experiments. Spectroscopic data of the ground state (v= 0, 1) was also available from accurate microwave experiments [14-16] for several isotopic species of the MgCl molecule. Nevertheless, the limited resolution of the optical experiments did not permit the direct observation of the spin-doubling splitting in the 0-0 band, nor assignments for the isotopic molecule ²⁴Mg³⁷Cl transitions, of the A²P-X²S⁺ system.

It was only recently that the A²P-X²S⁺ system could be studied by means of the high resolution Fourier Transform Spectroscopy. The emission spectra was produced in Orsay and Waterloo by using different techniques, and the strong similarity of the obtained spectra have allowed a joint analysis [17]. A complete rovibrational analysis of the A²P-X²S⁺ 0-0 and 0-1 bands, including vibrational dependence of the ground state and spin-orbit splitting of the A²P state, was carried out. The obtained value of the lambda doubling constant p was found positive, in contrast with the theoretical predictions [18].

This work presents a complementary analysis of the data obtained earlier[17]. For the first time 56 transitions of the ²⁴Mg³⁷Cl A²P-X²S⁺ 0-0 band could be assigned. A set of molecular constants, which reproduce the observed transitions of both ²⁴Mg³⁵Cl and ²⁴Mg³⁷Cl compounds, could be derived from a nonlinear least-squares fit of the optical data obtained from the Orsay group measurements.

2 The experiment

Excited MgCl species were produced in a Schüller's type tube which was heated in its middle part. More details of Schüller discharge device can be found elsewhere [19]. Briefly this discharge tube consists of a quartz tube for which both electrodes are located in front of a liquid nitrogen trap. In this way, electrodes are preventing of any contamination, resulting in a very stable discharge intensity. This light source is particularly convenient for emission Fourier Transform Spectroscopy. The MgCl molecules were produced in the following way: Mg pellets were introduced in the middle part of the discharge tube which was heated up to 800^oC, in order to obtain Mg vapor. The DC discharge (3400 V, 100 mA) was established through flowing He/Cl₂ gas mixture (1% of Cl₂ in He), at a pressure of 30 mbar. The spectrum was recorded by means of a Bruker IFS 120 HR Fourier Transform Spectrometer. The detector was a photo-multiplier tube (HAMAMATSU 1P28) associated with a long pass wavelength colored glass filter. The spectrum was obtained after the transformation of 1000 co-added interferograms recorded at an apodized resolution of 0.060 cm^-1.

3 Results

The observed high line density given by overlapping branches of this emission spectrum is a consequence of both the doublet structure of the involved electronic states and the very similar potential curve of the upper and lower states. In a A²P-X²S⁺ electronic transition one can expect to observe twelve branches for each band [20]. In addition these electronic states which have similar vibrational (and rotational) constants, result in sequences in which the separations of the bands are about 30 cm^-1.

An overview of a part of the obtained spectrum is shown in the Fig. 1. The A²P-X²S⁺ 0-0 band can be clearly seen in this figure, which shows the band head of the branches P₁₂, P₁₁, P₂₂, Q₂₂. Only transitions of the 0-1 A²P_1/2-X²S⁺ could be assigned in the sequence Dv = -1.

Rotational structure of the P₁₂ branches for both the ²⁴Mg³⁵Cl and the ²⁴Mg³⁷Cl isotopic species are shown in the Fig. 2. A total of 493 transitions was assigned, including 56 transitions of the not-predominant ²⁴Mg³⁷Cl isotopic species. These 56 transitions were assigned in the P₁₂, Q₁₁ and R₂₂ branches of the 0-0 band.

4 Analysis

Figure 3 shows a Fortrat diagram of the assigned transitions. This data set was analyzed in two different ways. In the first approach, the molecular constants were derived by adjusting all obtained data concerning both the 0-0 and 0-1 bands. In the second approach, the assigned lines of each band system were treated separately. In both analysis procedures, it was also possible to test the quality of the assignments taking into account the molecular constants of the ground state obtained from micro-wave experiments [14,15]. It was expected that the molecular constants calculated in this work should have a high coherence and complementarity with the very accurate constants derived in [14,15].

4.1 The Hamiltonian representation

The spectroscopic constants for the A²P and X²S⁺ electronic states were determined by a nonlinear least-squares fit of all observed wavenumbers. The energy term values of the X²S⁺ electronic state were described by a standard Hund's case "b" ²S⁺ formulae,

The Hamiltonian for the isolated A²P electronic state is shown in Table 1. The observed transitions involve only one vibrational level (v = 0) of the A²P state, consequently no vibrational dependence was taken into account in the Hamiltonian representation of this state. The data from the ²⁴Mg³⁷Cl molecule were included in the fit using standard transformation formulae [21]. An additional parameter Î was considered in the reductions. It was defined for the isotopic species as a slight change in the origin of the energies T,

r being the square root of the ratio between the reduced masses of ²⁴Mg³⁵Cl and ²⁴Mg³⁷Cl species, respectively.

4.2 The first approach: global reduction of the analysis data set

It appeared that no local perturbation affects the spectrum and, consequently a merged fit involving all observed transitions for the ²⁴Mg³⁵Cl and ²⁴Mg³⁷Cl isotopic species was performed in this work. A set of 14 molecular constants was derived, reproducing the observed transitions with a standard deviation less than 1.5×10^-2cm^-1. Tables 2(a) and 3(a) show the molecular constants issued from these calculations for the X²S⁺ and A²P states, respectively.

As a second global analysis procedure, a new adjust of the obtained global data set was performed, in which the ground state molecular constants B_e, a_B,b_B, g_e, g_v and g_B were held fixed in the values calculated by M. Bogey et al. [14]. The molecular constant values obtained by Bogey et al. [14] were used, instead of those obtained by Ohshima and Endo [15], because these parameters were derived in a data reduction merging all vibrational observed levels (v = 0, 1 and 2), allowing, therefore, a more adequate comparison between the results presented in this sub-section. All adjustable parameters of the A²P state, as well as the parameter w_e of the ground state, were left free in this new global data reduction. From this second procedure a set of 10 parameters was determined and no significant change in the r.m.s. of the adjust could be observed.

The values of the molecular constants for the ground state obtained by M. Bogey et al. [14], as well as the w_e value calculated in the procedure described above, are shown in Table 2 (column b). A strong coherence between the values listed in both Table 2 (column a) and Table 2 (column b) can be observed. The calculated molecular constants of the A²P excited state, obtained in the second analysis procedure described above, are shown in Table 3 (column b). Again a very good agreement between the molecular constant values shown in Table 3 (column a) and the ones shown in Table 3 (column b) can be noted.

4.3 The second approach: the independent reduction 0-0 and 0-1 band system data set

The data sets of the 0-0 and the 0-1 band systems were analyzed also separately. At first the 0-0 band was analyzed using the Hamiltonian described in the Section 4.1, in which the vibrational dependence was not taken into account. A set of 11 molecular constants was derived and it reproduced the observed transitions of the 0-0 band system within a standard deviation around 1.5×10^-2 cm^-1.

In the analysis involving the data of the 0-1 band system only transitions involving the A²P_1/2-X²S⁺ sub-band could be assigned. The spin orbit parameters A₀ and A_J were therefore held fixed in the value obtained from the analysis of the 0-0 band system. Also no lines concerning the ²⁴Mg³⁷Cl isotopic species were assigned in this band system. A set of 6 molecular constants was obtained in the data reduction, which reproduced the observed transitions of the 0-1 band system within a standard deviation around 1.5×10^-2 cm^-1. Tables 4(a) and 5(a) show the molecular constants for the X²S⁺ and A²P states respectively, issued from the calculations for each band system.

In an analogous analysis procedure described in the Section 4.2, a new adjust of the 0-0 and the 0-1 band system data was performed, in which the ground state molecular constants B_v, D_v,g_v and g_Dv were held fixed in the values obtained by Ohshima and Endo [15]. In this case, the choice of the molecular constants calculated in [15] instead of those calculated by Bogey et al. [14], is due to the fact that in the work of Ohshima and Endo each vibrational level (v = 0 and 1) has been fitted separately, allowing a more adequate comparison between the results presented in this sub-section. All adjustable parameters of the A²P state were left free in the adjust involving the 0-0 band system data set while those of the ground state were held fixed to the values reported in [15] for v"=0. From this second procedure a set of 10 parameters was calculated and no significant change in the r.m.s. of the adjust could be observed.

Also the 0-1 band system was analyzed by fixing the molecular constants B_v, D_v, g_v and g_Dv of the ground state in the values obtained by Ohshima and Endo [15] for v" = 1, and leaving the adjustable molecular constants of the A²P state as free parameters. A new set of 4 parameters, for the A²P state, was calculated from this procedure. No significant change in the r.m.s. of the adjust was observed.

The molecular constant values for the ground state obtained in [15] for v = 0 and v = 1 are shown in the Table 4(b). A reasonable agreement between the values listed in both Table 4(a) and Table 4(b) is observed. The calculated molecular constants of the A²P excited state, obtained in the 0-0 and 0-1 sub band analyses described above, are shown in Table 5(b). Once more a very good agreement between the molecular constant values calculated for the A²P state, shown in Tables 5(a) and Table 5(b), can be noted. Furthermore, Tables 4(c) and 5(c) show the values of the molecular constants obtained by M. Singh et al. [10] for both states. The differences between the obtained constants and the ones obtained in [10] are, to some extent, a consequence of different Hamiltonians used to represent the energy levels of the X²S⁺ and A²P states. In the analysis of M. Singh et al. [10] no spin-orbit value determination, nor the ²⁴Mg³⁷Cl isotopic species transitions were included.

5 Conclusion

The A²P-X²S⁺ band system of the MgCl molecule was studied by means of the Fourier Transform Spectroscopy (FTS). The MgCl molecules were produced by mixing Mg vapor with a gaseous flow of a He/Cl₂, and excited in a heated Schüller type discharge tube. An accurate set of molecular constants was determined from a complete rovibrational analysis of the 0-0 and 0-1 bands, including vibrational dependence on the ground state and spin-orbit splitting of the A²P state, and also by an independent 0-0 and 0-1 band system analysis. In both analysis procedures it was possible to take into account the molecular constants previously obtained [14,15] for the ground state, which were calculated with high accuracy. The high resolution of the FTS technique allows for the first time the observation and assignment of the ²⁴Mg³⁷Cl isotopic species transitions, which were included in the analysis presented in this work.

Acknowledgements

This work was partially supported by CAPES/COFECUB (Brazil/France cooperation) 182/96. One of the authors (C.E.F.) would like to thank CAPES/Brasil for a post-doctoral grant.

Received on 14 July, 2003

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Publication Dates

• Publication in this collection
  25 Nov 2005
• Date of issue
  Dec 2003

History

• Received
  14 July 2003
• Accepted
  14 July 2003