We present a method for calculating the infrared emission from a population of dust grains heated by starlight , including very small grains for which stochastic heating by starlight photons results in high temperature transients .
Because state-to-state transition rates are generally unavailable for complex molecules , we consider model PAH , graphitic , and silicate grains with realistic vibrational mode spectra and realistic radiative properties .
The vibrational density of states is used in a statistical-mechanical description of the emission process .
Unlike previous treatments , our approach fully incorporates multiphoton heating effects , important for large grains or strong radiation fields .

We discuss how the “ temperature ” of the grain is related to its vibrational energy .
By comparing with an “ exact ” statistical calculation of the emission process , we determine the conditions under which the “ thermal ” and the “ continuous cooling ” approximations can be used to calculate the emission spectrum .

We present results for the infrared emission spectra of PAH grains of various sizes heated by starlight .
We show how the relative strengths of the 6.2 , 7.7 , and 11.3 \micron features depend on grain size , starlight spectrum and intensity , and grain charging conditions .
We show results for grains in the “ cold neutral medium ” , “ warm ionized medium ” , and representative conditions in photodissociation regions .
Our model results are compared to observed ratios of emission features for the Milky Way and other galaxies , and for the M17 and NGC 7023 photodissociation regions .