  The accretion of hydrogen-rich matter onto C/O and O/Ne white dwarfs in
binary systems leads to unstable thermonuclear ignition of the accreted
envelope, triggering a convective thermonuclear runaway and a subsequent
classical, recurrent, or symbiotic nova. Prompted by uncertainties in the
composition at the base of the accreted envelope at the onset of convection, as
well as the range of abundances detected in nova ejecta, we examine the effects
of varying the composition of the accreted material. For high accretion rates
and carbon mass fractions < 0.002, we find that carbon, which is usually
assumed to trigger the runaway via proton captures, is instead depleted and
converted to 14N. Additionally, we quantify the importance of 3He, finding that
convection is triggered by 3He+3He reactions for 3He mass fractions > 0.002.
These different triggering mechanisms, which occur for critical abundances
relevant to many nova systems, alter the amount of mass that is accreted prior
to a nova, causing the nova rate to depend on accreted composition. Upcoming
deep optical surveys such as Pan-STARRS-1, Pan-STARRS-4, and the Large Synoptic
Survey Telescope may allow us to detect the dependence of nova rates on
accreted composition. Furthermore, the burning and depletion of 3He with a mass
fraction of 0.001, which is lower than necessary for triggering convection,
still has an observable effect, resulting in a pre-outburst brightening in disk
quiescence to > Lsun and an increase in effective temperature to 6.5e4 K for a
1.0 Msun white dwarf accreting at 1e-8 Msun/yr.
