  Plane-wave electronic-structure predictions based upon orbital-dependent
density-functional theory (OD-DFT) approximations, such as hybrid
density-functional methods and self-interaction density-functional corrections,
are severely affected by computational inaccuracies in evaluating electron
interactions in the plane-wave representation. These errors arise from
divergence singularities in the plane-wave summation of electrostatic and
exchange interaction contributions. Auxiliary-function corrections are
reciprocal-space countercharge corrections that cancel plane-wave singularities
through the addition of an auxiliary function to the point-charge electrostatic
kernel that enters into the expression of interaction terms. At variance with
real-space countercharge corrections that are employed in the context of
density-functional theory (DFT), reciprocal-space corrections are
computationally inexpensive, making them suited to more demanding OD-DFT
calculations. Nevertheless, there exists much freedom in the choice of
auxiliary functions and various definitions result in different levels of
performance in eliminating plane-wave inaccuracies. In this work, we derive
exact point-charge auxiliary functions for the description of molecular
structures of arbitrary translational symmetry, including the yet unaddressed
one-dimensional case. In addition, we provide a critical assessment of
different reciprocal-space countercharge corrections and demonstrate the
improved accuracy of point-charge auxiliary functions in predicting the
electronic levels and electrical response of conjugated polymers from
plane-wave OD-DFT calculations.
