Quasi-direct Quantum Molecular Dynamics: The Time-Dependent Adaptive Density-Guided Approach for Potential Energy Surface Construction

We
present a new quasi-direct quantum molecular dynamics computational
method which offers a compromise between quantum dynamics using a
precomputed potential energy surface (PES) and fully direct quantum
dynamics. This method is termed the time-dependent adaptive density-guided
approach (TD-ADGA) and is a method for constructing a PES on the fly
during a dynamics simulation. This is achieved by acquisition of new
single-point (SP) calculations and refitting of the PES, depending
on the need of the dynamics. The TD-ADGA is a further development
of the adaptive density-guided approach (ADGA) for PES construction
where the placement of SPs is guided by the density of the nuclear
wave function. In TD-ADGA, the ADGA framework has been integrated
into the time propagation of the time-dependent nuclear wave function
and we use the reduced one-mode density of this wave function to guide
when and where new SPs are placed. The PES is thus extended or updated
if the wave function moves into new areas or if a certain area becomes
more important. Here, we derive equations for the reduced one-mode
density for the time-dependent Hartree (TDH) method and for multiconfiguration
time-dependent Hartree (MCTDH) methods, but the TD-ADGA can be used
with any time-dependent wave function method as long as a density
is available. The TD-ADGA method has been investigated on molecular
systems containing single- and double-minimum potentials and on single-mode
and multi-mode systems. We explore different approaches to handle
the fact that the TD-ADGA involves a PES that changes during the computation
and show how results can be obtained that are in very good agreement
with results obtained by using an accurate reference PES. Dynamics
with TD-ADGA is essentially a black box procedure, where only the
initialization of the system and how to compute SPs must be provided.
The TD-ADGA thus makes it easier to carry out quantum molecular dynamics
and the quasi-direct framework opens up the possibility to compute
quantum dynamics accurately for larger molecular systems.