Calculation of the Temperature Dependence for Absorption in CO2in the 1750–1200 Å Region

Abstract

The absorption cross section of the diffuse absorption bands of CO₂ in the region 1750–1200 Å is of prime importance for understanding CO₂ photolysis, especially as a constituent of a planetary atmosphere. The upper state of the absorption is a ¹B₂ state correlating with a ¹Δ_u state in the linear geometry. Although the cross section for this vibronically allowed electric-dipole absorption will be temperature-dependent, there are no experimental studies of this temperature dependence, and room temperature values have been used in discussions of the atmospheres of Mars and Venus despite the widely disparate temperature distributions of their atmospheres. We have calculated the temperature dependence of the integrated absorption coefficient for the 1750–1200 Å region. The electronic energies and transition moments were calculated ab initio as a function of the bending angle of the molecule; in this way the Renner type splitting of the degenerate ¹Δ_u state into ¹B₂ and ¹A₂ energy curves is obtained. The integrated absorption cross section is proportional to the square of the transition moment averaged over the ground state vibrational wave functions. At room temperature the average of the transition moment squared over a Boltzmann distribution is 2.9 × 10⁻³ (ea₀)², which corresponds roughly to an oscillator strength of 6 × 10⁻⁴. Although halving the temperature produces only about 10% decrease in absorption, there is a dramatic increase by 75% when the temperature is doubled. The temperature dependence of individual lines, particularly in the wings of the overall distribution, is likely to be even more sensitive.