  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 $10^{-22}$
Watts for H$_2$O, CO$_2$, O$_3$, N$_2$O and CH$_4$ and of order $10^{-21}$
Watts 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.
