  We present a radiative transfer code to model the nebular phase spectra of
supernovae (SNe) in non-local thermodynamic equilibrium (NLTE). We apply it to
a systematic study of Type Ia SNe using parameterized 1D models and show how
nebular spectral features depend on key physical parameters, such as the time
since explosion, total ejecta mass, kinetic energy, radial density profile, and
the masses of 56Ni, intermediate mass elements (IMEs), and stable iron-group
elements (IGEs). We also quantify the impact of uncertainties in atomic data
inputs. Among the results of the study are: (1) The main features of SNe Ia
nebular spectra are relatively insensitive to most physical parameters.
Degeneracy among parameters precludes a unique determination of the ejecta
properties from spectral fitting. In particular, features can be equally well
fit with generic Chandrasekhar mass (M_ch), sub-M_Ch, and super-M_Ch models;
(2) A sizable (~0.1 Msun) central region of stable IGEs, often claimed as
evidence for M_Ch models, is not essential to fit the optical spectra and may
produce an unusual flat-top [CoIII] profile; (3) The strength of [SIII]
emission near 9500A can provide a useful diagnostic of explosion
nucleosynthesis; (4) Substantial amounts (~0.1 Msun) of unburned C/O mixed
throughout the ejecta produce [OIII] emission not seen in observations; (5)
Shifts in the wavelength of line peaks, sometimes used to infer ejecta
geometry, can also arise from line blending effects; (6) The steepness of the
ejecta density profile affects the line shapes, with flatter slopes providing
better fits to the observations of SN 2011fe, offering a constraint on
explosion models; (7) Uncertainties in atomic data affect spectral line ratios
by ~30%, a level similar to the effect of varying physical parameters.
