Direct-potential-fit analysis for the A3Π1uX1Σg+ system of Br2

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Abstract

Doppler-limited rovibrational absorption spectra of the A3Π1uX1Σg+ electronic transition of Br2 are measured in the 12 072–14 249 cm−1 region by a tone burst modulation method using a Ti:sapphire ring laser. P-, Q-, and R-branch lines belonging to the v   v = (2–16)  (2–8) bands of 79,79Br2 and 79,81Br2, and the v   v = (2–5)  6 bands of 81,81Br2 are observed and assigned. Accurate analytic potential energy functions for the A3Π1u and X1Σg+ states are determined from a combined-isotopologue direct-potential-fit analysis of these data together with all other available high quality data for the A and X states. This work also yields a slightly improved ground-state well depth De(X)=16056.875(2)cm-1 and dissociation energy D0(X)=15894.495(2)cm-1 for 79,79Br2, and shows that the isotope shift of the AX electronic transition energy Te81,81Te79,79=-0.016(3)cm-1 is likely mainly due to the isotopologue dependence of theX-state well depth.

Highlights

► 9334 New Br2 (AX) laser absorption measurements spanning v(X) = 2–8 and v(A) = 2–16. ► 2992 New magnetic rotation Br2 (AX) transitions for v(X) = 0–2  v(A) = 13–37. ► A direct potential-fit (DPF) analysis yields accurate, fully analytic potential energy functions for both states. ► The AX electronic isotope shift is Te81,81Te79,79=-0.016(3)cm-1. ► An improved ground-state well depth is De(X)=15894.495(2)cm-1.

Introduction

The A3Π1uX1Σg+ system of Br2 has been studied by many researchers. It was first observed in 1926 by Kuhn [1] and Nakamura [2] who published vibrational analyses of its absorption spectrum in the 5117–6722 and 5130–7586 Å regions, respectively. In 1931 Brown extended their results by using a grating spectrometer to study Br2 absorption in the 5100–7600 Å region, and reported vibrational assignments for band heads that he tentatively identified as being associated with v = 0–21 and v = 1–5 [3]. Five years later Darbyshire used a prism instrument to study high temperature samples in the 7600–8180 Å region [4]. This allowed him to extend the ground-state vibrational range to v = 13 and to observe two A-state vibrational levels lying below the lowest one that Brown had seen.

The first rotational analysis for the A3Π1uX1Σg+ system was reported by Horsley in 1967 [5]. He measured the absorption spectrum of natural bromine in the 6400–7100 Å region, and assigned the Q-branch lines of bands identified as v  v = (13–19)  2 and (16, 17)  3 of 79,81Br2. However, the absolute vibrational numbering for the A state remained unclear. In that same year Clyne and Coxon measured the band structure of Br2 in the 6400–10 000 Å region in emission, but again the absolute vibrational numbering in the A state remained unsettled [6]. Finally, in 1970 Coxon and Clyne measured the absorption spectrum of a few bands of isotopically pure 79,79Br2 with rotational resolution [7], and by comparing their results with the 79,81Br2 measurements of Horsley [5], they confirmed Darbyshire’s hypothesis [4] that the tentative A-state vibrational labels proposed by Brown [3] should be increased by seven. Shortly after this, Coxon extended his rotational resolution studies of the A3Π1uX1Σg+ system to span almost 50% of the A-state well (v = 7–24) [8], and reported extended sets of Franck–Condon factors and R-centroids for this system [9]. These studies provided a good basic understanding of the A3Π1u state of Br2, and facilitated its use in studying a number of ion-pair states [10], [11], [12], [13], [14], [15]. Moreover, one of these studies of ion-pair states reported a handful of observations of A-state levels v = 30–35 [10], and another reported observations of v(A) = 0 [15]. However, all of this early work has since been superseded by measurements of higher precision spanning an even wider range of levels. An overview of the data, on which the present analysis is based, is presented in Table 1. The average relative discrepancies shown in its second-last column are based on the final recommended potential energy function model of Section 4. The fact that all values of this average relative discrepancy are ≪1 shows that there are no significant calibration error inconsistencies among the various data subsets.

In 1999 Boone used Doppler-limited magnetic rotation spectroscopy with a dye laser [16], [17] to measure and assign some 3263 lines of 51 bands in the A3Π1uX1Σg+ spectrum of 79,79Br2, involving A-state vibrational levels v = 13–37. The highest vibrational level he observed is bound by only 2 cm−1. This is less than half the binding energy of the highest observed level of the B3Π0u+ state [18], and hence should allow an improved determination of the Br2 dissociation energy. Boone performed both a conventional Dunham expansion analysis and a ‘Near-Dissociation-Expansion’ analysis, and those results can be found in his thesis [16]. However, the lowest observed level of the A state was still v(A) = 7 [8], which lies almost 1000 cm−1 above the A-state potential minimum.

In the present work, rovibrational absorption spectra of the A  X transition of Br2 were measured in the 12 072–14 249 cm−1 region, and P-, Q-, and R-branch progressions of 109 bands in this system were assigned. The observed vibrational levels of 79,79Br2 and 79,81Br2 in the A and X state are v = 2–16 and v = 2–8, respectively, and those of 81,81Br2 are v = 2–5 and v = 6, while the associated rotational sublevels range up to J = 99. Thus, the high-resolution data (uncertainties <0.01 cm−1) for the A state used in the present analysis extend from v(A) = 2–37, with the highest observed vibrational level lying less than 2 cm−1 below the dissociation limit. A schematic overview of this system is presented in Fig. 1.

Unfortunately, the high-resolution AX data described above only span a small portion of the X1Σg+ state potential well (v = 0–8). Since we wish also to obtain the best possible overall description of the X1Σg+ ground state, the present analysis also incorporated the laser-induced fluorescence Fourier Transform (FT) results of Focsa et al. [19] for the BX system, which extend from v(X) = 2–29 for 79,81Br2 and from v(X) = 3–29 for 79,79Br2 and 81,81Br2. Following Focsa et al., our analysis also incorporates the 1515 synthetic term values for levels v = 0–14 of the ground state of 79,79Br2 that they had generated from the molecular constants of Gerstenkorn et al. [18], and treated as a synthetic fluorescence series. However, even with this inclusion, the data range only span 54% of the ground-state potential well.

More recently, Postell et al. performed laser-induced fluorescence measurements that extended this range to v(X) = 44, which is 75% of the way to dissociation [20], [21]. Although their data have relatively low precision (±0.27 cm−1), since they include results for all three isotopologues and extend the range to cover 3/4 of the potential well, they are also used in our analysis (weighted appropriately). The final set of X-state data included in the present analysis were then the 12 VUV resonance fluorescence series reported in 1982 by Venkteswarlu et al. [22]. Although these data span the range v =  0–76, they were pointedly omitted from the analysis of Focsa et al. because the 1982 molecular constants seemed inconsistent with their new higher accuracy (±0.01 vs. ±0.06 cm−1) FT results for v = 2–29 [19]. However, although the constants may be inconsistent, we find that within the reported uncertainties, the actual VUV data are entirely compatible with the higher resolution data. Hence, these VUV fluorescence series data were also utilized in the present analysis. As a result, our data for the X1Σg+ state span 99.2% of the ground-state potential well, with the highest observed level (v = 76) being bound by 129 cm−1. However, since the A3Π1u and X1Σg+ states have the same asymptote, the present analysis should yield an improved estimate of the ground-state dissociation energy.

In the following, Section 2 describes our new laser absorption measurements for the three isotopologues of Br2. Section 3 then describes our method of analysis and the models used for the potential energy and Born–Oppenheimer breakdown functions, while Section 4 presents our results.

Section snippets

Methodology

Fig. 2 presents a schematic view of the experimental setup. A titanium sapphire ring laser (Coherent, 899-21) pumped by an argon ion laser (Coherent, Innova 300) was used to obtain our Doppler limited absorption spectra. The absorption occurred in a White-type cell with an effective path length of 13.6 m that was filled with Br2 gas at 10 Torr, with the three isotopologues present in natural abundance. Measurements at wavelengths shorter than 0.77 μm, were made with the cell at room temperature,

Methodology

The main part of the present analysis was performed using a direct-potential-fit (DPF) method in which simulated spectra generated using a radial Hamiltonian H^=H^({pj}) defined in terms of parameterized potential energy, Born–Oppenheimer breakdown (BOB), and Ω-doubling strength functions, are compared with experiment, and the parameters {pj} are optimized by a standard non-linear least-squares-fit technique [29]. The partial derivatives of the eigenvalues with respect to the parameters of the

Results

Our challenge now is to determine the optimum form and polynomial order for the functions used to represent the exponent coefficients of the two MLR potentials, and for the A-state centrifugal BOB and Ω-doubling radial strength functions. Because fits in which one state or the other was represented by term values were relatively time consuming, we began with a cyclic approach of, in turn, optimizing the fit with regard to the parameters defining one of these states while holding the model for

Discussion

In many of the studies of the B(3Π0u+)-state halogens, it became commonplace to use near-dissociation theory analyses [56], [57], [58], [59] to obtain optimal estimates of the distance from the highest observed level to dissociation, of the number and energies of ‘missing’ levels, and of the leading long-range potential energy coefficient, C5. However, the distance at which the C5/r5 term becomes the dominant contribution to the long-range potential is almost an order of magnitude larger for

Acknowledgments

We are very grateful to Mr. David Postell and Professor David Dolson for permitting us to use their unpublished BX emission data in our analysis. C.B. and I.O. also very gratefully acknowledge enriching discussions with Professor F.W. Dalby. We also thank Professor Scott Hopkins for his patient assistance with Fig. 2. R.J.L., C.D.B. and I.O. are pleased to acknowledge financial support by the Natural Sciences and Engineering Research Council of Canada.

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