The Behavior of Selected Diffuse Interstellar Bands with Molecular
  Fraction in Diffuse Atomic and Molecular Clouds
  We study the behavior of eight diffuse interstellar bands (DIBs) in different
interstellar environments, as characterized by the fraction of hydrogen in
molecular form [$f$(H$_2$)], with comparisons to the corresponding behavior of
various known atomic and molecular species. The equivalent widths of the five
"normal" DIBs ($\lambda\lambda$5780.5, 5797.1, 6196.0, 6283.8, and 6613.6),
normalized to $E(B-V)$, show a "Lambda-shaped" behavior: they increase at low
$f$(H$_2$), peak at $f$(H$_2$) ~ 0.3, and then decrease. The similarly
normalized column densities of Ca, Ca$^+$, Ti$^+$, and CH$^+$ also decline for
$f$(H$_2$) > 0.3. In contrast, the normalized column densities of Na, K, CH,
CN, and CO increase monotonically with $f$(H$_2$), and the trends exhibited by
the three C$_2$ DIBs ($\lambda\lambda$4726.8, 4963.9, and 4984.8) lie between
those two general behaviors. These trends with $f$(H$_2$) are accompanied by
cosmic scatter, the dispersion at any given $f$(H$_2$) being significantly
larger than the individual errors of measurement. The Lambda-shaped trends
suggest the balance between creation and destruction of the DIB carriers
differs dramatically between diffuse atomic and diffuse molecular clouds;
additional processes besides ionization and shielding are needed to explain
those observed trends. Except for several special cases, the highest
$W$(5780)/$W$(5797) ratios, characterizing the so-called "sigma-zeta effect",
occur only at $f$(H$_2$) < 0.2. We propose a sequence of DIBs based on trends
in their pair-wise strength ratios with increasing $f$(H$_2$). In order of
increasing environmental density, we find the $\lambda$6283.8 and
$\lambda$5780.5 DIBs, the $\lambda$6196.0 DIB, the $\lambda$6613.6 DIB, the
$\lambda$5797.1 DIB, and the C$_2$ DIBs.
