A considerable effort has been recently directed towards developing
separable (mean-field) approximations for quantum molecular
dynamics, such as the Time-Dependent
Self-Consistent Field (TDSCF) or the Classical Separable Potential (CSP) methods.
Unlike numerically exact solutions of the time-dependent Schrodinger
equation, the accuracy of separable quantum dynamical simulations
crucially depends on the choice of the coordinate frame. Since the approximate methods
replace exact interactions between individual degrees of freedom by mean-field
couplings the goal is to work with coordinates which separate modes as well as
possible. Unfortunately, for larger system no practical way to optimize
coordinates for mean-field quantum dynamics exists.
Here, we suggest a simple and practical method for estimating the error
of separable simulations,
which allows to select from a given set the optimal coordinate frame, or to identify
modes the couplings between which have to be treated more accurately.
In the spirit of the CSP method, the time-dependent error estimate
is based on differences between the exact and mean-field Hamiltonians along a swarm
of classical trajectories. This makes it possible to very simply determine optimal coordinates for
CSP or TDSCF propagation before actually performing any quantum simulation.
The present methodology is applied to realistic and experimentally
relevant systems, namely to the ultrafast relaxation following electron photodetachment
in I-Arn (n=2 and 12) and Cl-H2O clusters.
It is shown that the accuracy of separable quantum methods
is strongly system and coordinate dependent. Comparison with numerically
exact results shows that the suggested
error measure correlates well with the actual error of the approximate quantum
propagation, the accuracy of which can be consequently improved significantly,
practically without additional computational effort. Finally, the feasibility
of the proposed method for simulations of large polyatomic systems
is demonstrated.