An accurate and computationally efficient approach to evaluate wide band parameters with polynomial series for use in a simplified wide band cumulative absorption coefficient distribution, g(k), model is presented. The fitting coefficients are determined by a best fit with g(k) functions generated from the latest high resolution spectroscopic database. The approach significantly improves the prediction of the g(k) function over a wide range of temperatures from 500 to 2500 K, pressures from 0.01 to 1.0 atm, and all single bands of H2O and CO2. The root mean square error of the predicted absorption coefficient is below 25% except the single 4.3 Pm band model. The approach also provides accurate calculations for the wide band absorptance, generally with differences below 7% when compared to benchmark results. (C) 2007 Published by Elsevier Ltd.