MCTDH: To Be Done

• Out of order
• To be done
• Outlook

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To Be Done

Out of order

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.

To be done

• 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 entered.
• 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 CMF integrator.
• 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 implemented.
• The improved error estimate for the Lanczos-Arnoldi integrator should be implemented also in the Hermitian Lanczos integrator.
• 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 packets.
• 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 that.
• 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.

Outlook

Where do we want to go tomorrow? Here some ideas of how the MCTDH method may be developed further are given.

Cascading:

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.