  The earliest atmospheres of rocky planets originate from extensive volatile
release during magma ocean epochs that occur during assembly of the planet.
These establish the initial distribution of the major volatile elements between
different chemical reservoirs that subsequently evolve via geological cycles.
Current theoretical techniques are limited in exploring the anticipated range
of compositional and thermal scenarios of early planetary evolution, even
though these are of prime importance to aid astronomical inferences on the
environmental context and geological history of extrasolar planets. Here, we
present a coupled numerical framework that links an evolutionary,
vertically-resolved model of the planetary silicate mantle with a
radiative-convective model of the atmosphere. Using this method we investigate
the early evolution of idealized Earth-sized rocky planets with end-member,
clear-sky atmospheres dominated by either H$_2$, H$_2$O, CO$_2$, CH$_4$, CO,
O$_2$, or N$_2$. We find central metrics of early planetary evolution, such as
energy gradient, sequence of mantle solidification, surface pressure, or
vertical stratification of the atmosphere, to be intimately controlled by the
dominant volatile and outgassing history of the planet. Thermal sequences fall
into three general classes with increasing cooling timescale: CO, N$_2$, and
O$_2$ with minimal effect, H$_2$O, CO$_2$, and CH$_4$ with intermediate
influence, and H$_2$ with several orders of magnitude increase in
solidification time and atmosphere vertical stratification. Our numerical
experiments exemplify the capabilities of the presented modeling framework and
link the interior and atmospheric evolution of rocky exoplanets with
multi-wavelength astronomical observations.
