  We explore an alternative to twist averaging in order to obtain more
cost-effective and accurate extrapolations to the thermodynamic limit (TDL) for
coupled cluster doubles (CCD) calculations. We seek a single twist angle to
perform calculations at, instead of integrating over many random points or a
grid. We introduce the concept of connectivity, a quantity derived from the
non-zero four-index integrals in an MP2 calculation. This allows us to find a
special twist angle that provides appropriate connectivity in the energy
equation, and which yields results comparable to full twist averaging. This
special twist angle effectively makes the finite electron number CCD
calculation represent the TDL more accurately, reducing the cost of
twist-averaged CCD over $N_\mathrm{s}$ twist angles from $N_s$ CCD calculations
to $N_s$ MP2 calculations plus one CCD calculation.
