  The generalized Kadanoff-Baym ansatz (GKBA) offers a computationally
inexpensive approach to simulate out-of-equilibrium quantum systems within the
framework of nonequilibrium Green's functions. For finite systems the
limitation of neglecting initial correlations in the conventional GKBA approach
has recently been overcome [Phys. Rev. B 98, 115148 (2018)]. However, in the
context of quantum transport the contacted nature of the initial state, i.e., a
junction connected to bulk leads, requires a further extension of the GKBA
approach. In this work, we lay down a GKBA scheme which includes initial
correlations in a partition-free setting. In practice, this means that the
equilibration of the initially correlated and contacted molecular junction can
be separated from the real-time evolution. The information about the contacted
initial state is included in the out-of-equilibrium calculation via explicit
evaluation of the memory integral for the embedding self-energy, which can be
performed without affecting the computational scaling with the simulation time
and system size. We demonstrate the developed method in carbon-based molecular
junctions, where we study the role of electron correlations in transient
current signatures.
