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Least-squares analysis of overlapped bound-free absorption spectra and predissociation data in diatomics: The C(1Π u ) state of I2
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Image of FIG. 1.
FIG. 1.

Visible absorption spectrum (molar absorptivity) of gaseous I2 near room temperature, with component bands (top), and potential diagram relevant to the absorption. In the spectra, broken curves illustrate results from Ref. 10, while solid curves are current results. In the potential diagram, broken curves illustrate regions known from discrete spectroscopy, and vertical dashed lines delimit absorption region. Energies are relative to lowest dissociation limit. Spectra are computed using the pseudocontinuum model.

Image of FIG. 2.
FIG. 2.

Absorbance as a function of concentration at selected wavelengths, for a cell at 35 °C having a path length of 9.93(3) cm. The absorption is purely continuous at 490 nm, and mainly discrete at 530 nm; at 650 nm (scaled for display purposes), the absorption is about 80% continuous and 20% from densely overlapped lines of the BX system. The data include blanks at zero concentration. The curves show least-squares fits to straight lines and to a quadratic (530 nm), with intercepts included in both fit models.

Image of FIG. 3.
FIG. 3.

I2 molar absorptivity, as estimated from linear and quadratic fits of absorbance data recorded at 2-nm intervals, I2 pressures 0–400 mTorr, and a cell temperature of 35 °C. The upper panel illustrates the estimated standard deviations from these fits, carried out at each wavelength. Where the linear and quadratic fits diverge in slope, the data are not following Beer's Law; where σ A rises anomalously (510–580 nm), not even the slope of the quadratic analysis can be trusted as a reliable low-A estimate of ɛ.

Image of FIG. 4.
FIG. 4.

Effects of various treatments on the repulsive branch of the B-state potential curve. Each R shift is referenced to the RKR potential computed from the constants given in Refs. 3 and 32, as R(RKR) − R. Note the 10-fold magnification of the RKR-IPA differences; the irregular behavior beyond 4200 cm−1 is attributable to the RKR curve.

Image of FIG. 5.
FIG. 5.

Estimates of continuum absorptivity in region of discrete BX absorption (points, Ref. 16, two sets of experiments) compared with estimates of the total (solid curve) and component bands (dashed) obtained from present analysis of spectra at two temperatures.

Image of FIG. 6.
FIG. 6.

BX transition strengths from Ref. 16 (points, two sets of experiments), compared with results from present analysis for a fit model having 2, 1, and 2 adjustable parameters in Eq. (4), for the A, B, and C states, respectively. The curves represent results obtained using just the average J (solid) and averaging over 5 J levels (dashed) in the analysis of spectra at two temperatures.

Image of FIG. 7.
FIG. 7.

I2 B and C potentials relevant to BC predissociation (below), and statistical error in the C potential (above). LS-fitted C curves: 1 – U C = −41 + 9.69 × 107/R 9.606; 2 – U C = −2155 + 6.55 × 106/R 6.64. Error curves (above; note logarithmic scale): solid – from spectral fitting using a 4-parameter exponential polynomial; dashed – predissociation fitting yielding curve 1. Energies are relative to the first dissociation limit. B-state vibrational levels 10−40 are shown; the B/C crossing occurs just above υ B = 2.

Image of FIG. 8.
FIG. 8.

Rate coefficients for magnetic predissociation from Ref. 24 and fitted results from C potential curves 1 (solid) and 2 (dashed) shown in Fig. 7. For large υ B , where the rate data represent a range of levels, the errors have been expanded to include the effect of the υ B uncertainty. The two fits gave reduced χ 2 values of 4.04 (solid) and 2.89.

Image of FIG. 9.
FIG. 9.

Quantal properties of RKR B-state potential (dashed) and its modification as obtained from spectral fitting with exponential polynomial attached at υ = 33 (solid). Plotted quantities are computed – spectroscopic. The combined vibrational and rotational energy excesses are comparable for the two curves at high υ and the upper limit of the J data field in Ref. 3. (The RKR curve is smoothed above υ = 61 with a potential of form 1/R,13 as indicated by its behavior at smaller υ.)

Image of FIG. 10.
FIG. 10.

Computed CX spectra for attachment of the small-R extension of the B potential at υ = 33 (with 1-σ error bars) and at υ = 46; and the uncertainty (1σ) in the total spectrum (scale right).

Image of FIG. 11.
FIG. 11.

Electronic transition moment functions for the BX and CX transitions. Broken curves represent results obtained attaching the B extension at υ = 46. Points are theoretical estimates from Ref. 43. The solid curve for BX is from Ref. 16. Error bars (shading) are 1σ.

Image of FIG. 12.
FIG. 12.

Model error (ΔU) and statistical error in B and C potential curves. The ΔU values are the differences between results obtained attaching the small-R B extension at υ = 46 and at υ = 33, in the sense U 46U 33. The statistical error in the B potential vanishes at the point of attachment to the RKR curve, as the latter is treated as error-free.


Generic image for table
Table I.

Least-squares analysis of I2 visible absorption and B-state predissociation.a

Generic image for table
Table II.

Computed molar absorptivity (l mol−1 cm−1) of I2(g) at 0 °C and at 35 °C.a


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Least-squares analysis of overlapped bound-free absorption spectra and predissociation data in diatomics: The C(1Πu) state of I2