  We explore the framework of a real-time coupled cluster method with a focus
on improving its computational efficiency. Propagation of the wave function via
the time-dependent Schr\"odinger equation places high demands on computing
resources, particularly for high level theories such as coupled cluster with
polynomial scaling. Similar to earlier investigations of coupled cluster
properties, we demonstrate that the use of single-precision arithmetic reduces
both the storage and multiplicative costs of the real-time simulation by
approximately a factor of two with no significant impact on the resulting
UV/vis absorption spectrum computed via the Fourier transform of the
time-dependent dipole moment. Additional speedups of up to a factor of 14 in
test simulations of water clusters are obtained via a straightforward GPU-based
implementation as compared to conventional CPU calculations. We also find that
further performance optimization is accessible through sagacious selection of
numerical integration algorithms, and the adaptive methods, such as the
Cash-Karp integrator provide an effective balance between computing costs and
numerical stability. Finally, we demonstrate that a simple mixed-step
integrator based on the conventional fourth-order Runge-Kutta approach is
capable of stable propagations even for strong external fields, provided the
time step is appropriately adapted to the duration of the laser pulse with only
minimal computational overhead.
