  The inherently high computational cost of iterative self-consistent-field
(SCF) methods proves to be a critical issue delaying visual and haptic feedback
in real-time quantum chemistry. In this work, we introduce two schemes for SCF
acceleration. They provide a guess for the initial density matrix of the SCF
procedure generated by extrapolation techniques. SCF optimizations then
converge in fewer iterations, which decreases the execution time of the SCF
optimization procedure. To benchmark the proposed propagation schemes, we
developed a test bed for performing quantum chemical calculations on sequences
of molecular structures mimicking real-time quantum chemical explorations.
Explorations of a set of six model reactions employing the semi-empirical
methods PM6 and DFTB3 in this testing environment showed that the proposed
propagation schemes achieved speedups of up to thirty percent as a consequence
of a reduced number of SCF iterations.
