directions.

The physics of ions, molecules, and grains
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 was originally designed to simulate the dense gas found near the black hole and accretion disk in The so-called “Broad Line Region” (BLR) mainly emits in the UV and optical, and these spectral regimes were the original focus. Some investigations are @Rees1989, @FerlandPeterson1992, and @Baldwin1995. Lower density gas, at larger distances from the center, produces the “Narrow Line Region” (NLR) spectrum, which includes a range of forbidden and permitted lines in the UV, optical, and IR. The study by @Ferland1983 is an example. Such investigations drove the development of , as summarized in the 1998 review, although Photo-dissociation Region (“PDRs”) and X-ray Dissociation Regions (“XDRs”) were also simulated [@Ferland1994; @FerlandFabian2002].

The following sections describe our improvements in the treatment of ions, molecules, and grains since F98, by citing those papers which introduced the advances. This is not meant to be a comprehensive review of the literature, rather, only a description of advances to  since the last review.

Structure of the H-like and He-like iso-electronic sequences
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Hydrogen and helium are the most common elements in the universe and, as a result, need to be treated with the greatest precision. Their structure 