The forcings due to changing concentrations of Earth's five most important, naturally occurring greenhouse gases, H 2 O, CO 2 , O 3 , N 2 O and CH 4 as well as CF 4 and SF 6 were evaluated for the case of a cloud-free atmosphere. The calculation used over 1.5 million lines having strengths as low as 10 −27 cm. For a hypothetical, optically thin atmosphere, where there is negligible saturation of the absorption bands, or interference of one type of greenhouse gas with others, the per-molecule forcings are of order 10 −22 W for H 2 O, CO 2 , O 3 , N 2 O and CH 4 and of order 10 −21 W for CF 4 and SF 6 . For current atmospheric concentrations, the per-molecule forcings of the abundant greenhouse gases H 2 O and CO 2 are suppressed by four orders of magnitude. The forcings of the less abundant greenhouse gases, O 3 , N 2 O and CH 4 , are also suppressed, but much less so. For CF 4 and SF 6 , the suppression is less than an order of magnitude because the concentrations of these gases is very low. For current concentrations, the per-molecule forcings are two to four orders of magnitude greater for O 3 , N 2 O, CH 4 , CF 4 and SF 6 than those of H 2 O or CO 2 . Doubling the current concentrations of CO 2 , N 2 O or CH 4 increases the forcings by a few per cent. A concentration increase of either CF 4 or SF 6 by a factor of 100 yields a forcing nearly an order of magnitude smaller than that obtained by doubling CO 2 . Important insight was obtained using a harmonic oscillator model to estimate the power radiated per molecule. Unlike the most intense bands of the 5 naturally occurring greenhouse gases, the frequency-integrated cross sections of CF 4 and SF 6 were found to noticeably depend on temperature.