The nature of the carriers of the interstellar infrared (IR) emission features between 3.3 and 12.7 μm is complex. We must consider emission from a family of polycyclic aromatic hydrocarbons (PAHs) in a multiplicity of cationic charge states (+1, +2, +3, and so on), along with neutral and anionic PAHs. The adopted intrinsic IR cross sections of the various modes of the PAHs are the key to all models. Here we make a comparison between laboratory-measured cross sections and quantum chemical calculations and find that, overall, the agreement is very good. In this paper, we consider emission from a wide variety of specific PAH molecules, which includes all available data from our laboratory and quantum chemical databases. We incorporate this into our model to produce a theoretical analysis that is more realistic, detailed, and comprehensive than prior studies. PAH molecular structures that we consider include symmetric condensed, symmetric noncondensed, aromatics containing pentagonal rings, linear, and methylated PAHs. The synthesized IR spectra show large variations in peak position for the small PAHs studied, while their spectral profile is uniquely characteristic of each different molecular structure. We also investigate the spectral variations with molecular structure of a PAH population at the surface of the Orion photodissociation region (PDR) and include an example of how the IR spectrum of our PAH population varies dramatically as a function of depth (or radiation field) through the PDR. We make a comparison of these results with Infrared Space Observatory data measured at the surface of the Orion PDR. We conclude that the charge of PAHs in a composite population has a stronger effect on its IR emission spectrum than its molecular structure. However, on the basis of the PAH samples considered in this paper, detailed studies of the interstellar IR emission features can be used effectively to identify molecular characteristics of the interstellar PAH family. In Paper III, we extend the theme of this paper by investigating the effects of hydrogenation on a wide variety of PAHs up to size 54 carbon atoms and compare our results with observational profiles for the Orion PDR.