We present efficient adaptive numerical solution methods for systems of nonlinear Schrödinger
equations associated with the multiconfiguration time-dependent Hartree-Fock
method for the solution of the multi-electron time-dependent Schrödinger equation.
The methods in our focus comprise splitting methods, exponential integrators and
Lawson methods. We demonstrate that in the light of the high computational effort
for the evaluation of the nonlocal operator associated with the potential part,
Adams-Lawson multistep methods with a predictor/corrector step provide an optimal
work/precision relation and also stable long-term integration.
The corrector also provides an error estimator without additional computational effort,
and thus adaptive time-stepping can be realized. This is demonstrated to reflect
well the smoothness of the solution. Furthermore, the convergence
of Adams-Lawson multistep methods for the MCTDHF equations is proven theoretically under minimal
assumptions on the regularity of the exact solution.