  The nucleosynthesis in classical novae, in particular that of radioactive
isotopes, is directly measurable by its $\gamma$-ray signature. Despite decades
of observations, MeV $\gamma$-rays from novae have never been detected --
neither individually at the time of the explosion, nor as a result of
radioactive decay, nor the diffuse Galactic emission from the nova population.
Thanks to recent developments in modeling of instrumental background for MeV
telescopes such as INTEGRAL/SPI and Fermi/GBM, the prospects to finally detect
these elusive transients are greatly enhanced. This demands for updated and
refined models of $\gamma$-ray spectra and light curves of classical novae. In
this work, we develop numerical models of nova explosions using sub- and
near-Chandrasekhar CO white dwarfs as the progenitor. We study the parameter
dependence of the explosions, their thermodynamics and energetics, as well as
their chemical abundance patterns. We use a Monte-Carlo radiative transfer code
to compute $\gamma$-ray light curves and spectra, with a focus on the early
time evolution. We compare our results to previous studies and find that the
expected 511-keV-line flash at the time of the explosion is heavily suppressed,
showing a maximum flux of only $10^{-9}\,{\rm ph}\,$cm$^{-2}\,$s$^{-1}$ and
thus making it at least one million times fainter than estimated before. This
finding would render it impossible for current MeV instruments to detect novae
within the first day after the outburst. Nevertheless, our time-resolved
spectra can be used for retrospective analyses of archival data, thereby
improving the sensitivity of the instruments.
