To Be Done
This part of the documentation is intended to describe those
options of the MCTDH program that should but do not work due to
the laziness of the programmers. In particular, all known bugs
that have not been fixed so far should be reported here.
- Relaxation of density operators of
type I does not work properly. The relaxation often
converges, but to a (slightly) wrong result. Relaxation
of type II density operators is OK.
- The CMF integration scheme becomes less accurate (and
takes smaller update steps) when the WF enters a CAP. The
CMF integration scheme should be modified and improved
such that it performs equally well when a CAP is
- If a propagation employs natural orbitals, the
initial wavepacket should be transformed to natural
orbitals after being read from file, to allow the use of
standard orbitals in the preceeding relaxation.
- Implement CDVR with CMF integrator.
- Implement usage of multi-dimensional surfaces with
- The MCTDH program should be able to dynamically
increase or decrease the numbers of single-particle
functions during the propagation.
- In the CMF scheme, the equations of motion for the
single-particle functions are not variationally optimal
for the given equations of motion of the coefficients. A
different projector and a symmetric propagation of
single-particle functions and coefficients should be
- The improved error estimate for the Lanczos-Arnoldi
integrator should be implemented also in the Hermitian
- In a multi-packet run one may increase the efficiency
of the propagation and decrease the memory needed by not
propagating the various packets simultaneously. This
would require to reorder the wavefunction vector and
select the correct Hamiltonian terms for the individual
- In a multi-packet run it would be advantageous to use
different numbers of single-particle functions for the
various packets. Note that the computation of the
cross-correlation functions must be changed for
- The MCTDH program may take a large amount of memory,
if there are large combined grids and many Hamiltonian
terms (e.g. a large natpot). The reason is the hpsi
array. The application of the Hamiltonian to the WF
should be re-organized (make the loop over k to the
outermost loop) such that this problem disappears.
Where do we want to go tomorrow? Here some ideas of how the
MCTDH method may be developed further are given.
- Problems of very large dimensions (f = 30 ... 200)
may become feasible via extreme combinations yielding only 4 to
8 particles. The resulting high dimensional single-particle
functions may be propagated by an MCTDH-like scheme. In
principle this procedure can be iterated yielding a cascade of
MCTDH calculations. See H.-D. Meyer and G. A. Worth, Theor.
Chem. Acc. 109 (2003), 251, and H. Wang and M. Thoss,
J.Chem.Phys. 119 (2003), 1289.