Theoretical Studies of Partition Functions of Flue Gas $SO_2$-Isotope

Abstract

The geometrical structure of flue gas $^{32}S^{16}O_2$ and $^{34}S^{16}O_2$ molecule have been optimized at B3P86/cc-PV5Z level using Gaussian03 program, we gain their equilibrium geometry, resonance frequency and rotational constants et al.. The total internal partition functions are calculated at the temperatures from 70 K to 6000 K for $^{32}S^P{16}O_2$ and $^{34}S^{16}O_2$ with the product approximation. Thereinto, the rotational partition sums $Q_{rot}$ adopt the WATSON rigid rotator model, which take into account centrifugal distortion corrections. The vibrational partition sums $Q_{vib}$ use the harmonic oscillator approximation model. It is found that the calculated total internal partition functions are consistent with those offered by HITRAN database from 70 K to 3000 K, and the errors shows linear correlation approximately. By fitting the errors, the total internal partition functions values at high temperature range of 3000 K to 6000 K were corrected. The corrected total internal partition functions are fitted to a four-order polynomial expression in $T,$ and the coefficients are gained at high temperature. This allows a rapid and accurate calculation of the total internal partition functions at the temperature from 3000 K to 6000 K.