Diatom potential curves and transition moment functions from continuum absorption coefficients: Br2

Abstract

A program for calculating diatomic molecule absorption coefficients using ’’exact’’ numerically computed radial wavefunctions was developed and used to examine critically a number of approximations which are frequently used in absorption coefficient calculations. These tests showed that both use of the delta function approximation, and fixing the rotational quantum number in the radial overlap integrals at J=0, introduce errors of ?4%–6% of the absorption coefficient maximum ε^max. Similarly, errors of ?1%–2% of ε^max are introduced by either fixing the initial state J at the average value for the given temperature, or by using Gislason’s Airy‐function approximation for the unbound state wavefunction. A simple procedure for shrinking the sum over initial state J’s without significant loss of accuracy was therefore devised. These techniques were then applied to the analysis of the visible absorption continuum of Br₂, and a nonlinear least‐squares fitting procedure used to determine optimized final state potential curves and transition moment functions for the two overlapping electronic transitions. In the region to which the data are sensitive, 2.10≲R≲2.55 Å, the transition moments so obtained (in debyes, lengths in angstroms) are M₀(R) =0.3905+0.265(R−2.3) for the B (³Π⁺_Ou) ←X (¹Σ⁺_g) transitions and M₁(R) =0.5060–0.154(R−2.3) for the ¹Π_1u←X (¹Σ⁺_g) spectrum. The concomitant repulsive potential curves for the B (³Π⁺_Ou) and ¹Π_1u states are, respectively (in cm⁻¹, expressed relative to the ground state dissociation limit; lengths in angstroms): V₀(R) =−1174+5494 exp[−5.807(R−2.3)] and V₁(R) =7654 exp[−4.637(R−2.3)−0.879(R−2.3)²], where the former expression applies only to the region inside the B‐state inner turning point for v=8, R₁(8) =2.4485 Å. Comparisons with experimental relative intensities in the discrete portion of the B–X spectrum, and with molecular beam photofragment spectroscopy measurements of the relative strengths of the two electronic transitions, are also reported.