  We have conducted a large-scale survey of 120 planetary nebulae (PNe) to
search for the near-infrared emission lines [Kr III] 2.199 and [Se IV] 2.287
microns. The neutron(n)-capture elements Se and Kr may be enriched in a PN if
its progenitor star experienced s-process nucleosynthesis and third dredge-up.
In order to determine Se and Kr abundances, we have added these elements to the
atomic databases of the photoionization codes Cloudy and XSTAR, which we use to
derive ionization correction factors (ICFs) to account for the abundances of
unobserved Se and Kr ions. However, much of the atomic data governing the
ionization balance of these two elements are unknown, and have been
approximated from general principles. We find that uncertainties in the atomic
data can lead to errors approaching 0.3 dex in the derived Se abundances, and
up to 0.2--0.25 dex for Kr. To reduce the uncertainties in the Kr ionization
balance stemming from the approximate atomic data, we have modeled ten bright
PNe in our sample, selected because they exhibit emission lines from multiple
Kr ions in their optical and near-infrared spectra. We have empirically
adjusted the uncertain Kr atomic data until the observed line intensities of
the various Kr ions are adequately reproduced by our models. Using the adjusted
Kr atomic data, we have computed a grid of models over a wide range of physical
parameters (central star temperature, nebular density, and ionization
parameter), and derived formulae that can be used to compute Se and Kr ICFs. In
the second paper of this series, we will apply these ICFs to our full sample of
120 PNe, which comprises the first large-scale survey of n-capture elements in
PNe.
