  We investigate the numerical stability of time-dependent coupled-cluster
theory for many-electron dynamics in intense laser pulses, comparing two
coupled-cluster formulations with full configuration interaction theory. Our
numerical experiments show that orbital-adaptive time-dependent coupled-cluster
doubles (OATDCCD) theory offers significantly improved stability compared with
the conventional Hartree-Fock-based time-dependent coupled-cluster
singles-and-doubles (TDCCSD) formulation. The improved stability stems from
greatly reduced oscillations in the doubles amplitudes, which, in turn, can be
traced to the dynamic biorthonormal reference determinants of OATDCCD theory.
As long as these are good approximations to the Brueckner determinant, OATDCCD
theory is numerically stable. We propose the reference weight as a diagnostic
quantity to identify situations where the TDCCSD and OATDCCD theories become
unstable.
