MCTDH stands for Multi Configuration Time Dependent Hartree. MCTDH is a general algorithm to solve the time-dependent Schrödinger equation for multidimensional dynamical systems consisting of distinguishable particles. MCTDH can thus determine the quantal motion of the nuclei of a molecular system evolving on one or several coupled electronic potential energy surfaces. MCTDH by its very nature is an approximate method. However, it can be made as accurate as any competing method, but its numerical efficiency deteriorates with growing accuracy.

MCTDH is designed for treating multi-dimensional problems, in particular problems that are difficult or even impossible to attack in a conventional way. There is no or only little gain when treating systems with less than three degrees of freedom by MCTDH. However, for convenience − not for numerical speed − be have used the MCTDH package even for one-dimensional problems. MCTDH will in general be best suited for systems with 4 to 12 degrees of freedom. Because of hardware limitations it may in general not be possible to treat much larger systems. For a certain class of problems, however, one can go much further. Already some time ago (1998/1999) we have performed converged MCTDH calculations on the absorption spectrum of pyrazine accounting for the motion of all 24 (!) internal degrees of freedom. Similar calculations have been done for the ionisation spectra of Allene, Butatrien and Benzene. The spin-boson model was treated by Haobin Wang including 80 vibrational modes, and we have recently used MCTDH to study the multi-dimensional Henon-Heiles Hamiltonian including up to 32 degrees of freedom and a Morse oscillator coupled to a harmonic bath including up to 61 degrees of freedom.
The MCTDH program package has been generalised to enable the propagation of density operators, and recently it has been generalized to compute eigenstates ("improved relaxation").

MCTDH has the following advantages

- The MCTDH algorithm can be very fast. In fact it may be several orders of magnitude faster than a conventional treatment. Whether MCTDH is fast or not depends on the system under consideration (see below).
- The MCTDH algorithm is small, i.e it requires an amazingly small amount of central memory (RAM). The MCTDH representation of the wave function is also very compact, making it possible to store a large number of wave functions for later analysis.

MCTDH has the following disadvantages

- The MCTDH algorithm requires the Hamiltonian to be expanded as a sum of products of one-particle operators. The kinetic energy is usually already in this MCTDH form. The potential is in MCTDH form only when dealing with model problems. In general one has to transform the potential (obtained e.g. by quantum chemistry calculations) to MCTDH form. There exist an efficient algorithm to accomplish this transformation. However, the MCTDH computation time grows linearly with the number of Hamiltonian terms and MCTDH will become slow, if an accurate representation of the potential requires very many terms.
- The MCTDH algorithm is fast only if the time dependent wavepacket can - at each instant of time - be expanded into a small (but optimised) product basis set. This makes it difficult for MCTDH to propagate a wavepacket when the system is highly chaotic. It is also difficult for MCTDH to propagate a wavepacket for very long times (hundreds of vibrational periods, say). However, we recently [70] have propagated a wavepacket on a 4D Henon-Heiles potential over 300 time units (i.e. about 50 vibrational periods). Thus even a chaotic system may be studied for rather long times. The 14D Henon-Heiles potential was also investigated. Here the propagation was stopped after 25 time units, as this was enough to reproduce the spectrum.

## Using MCTDH on Kogence

You can either fork and modify an existing MCTDH public project or alternatively you can also start from scratch and create a new MCTDH project.

- In order to fork an existing project
- Make sure you fist click "Copy" button to create a personal copy to modify.
- Then click Settings -> Machine to choose a machine and
- Click Settings -> Software and choose MCTDH from the dropdown menu.
- In the empty text box, type the name of the input script without the *.inp extension.
- Alternatively, you can type "xterm" in the empty text box to get a shell terminal with MCTDH access. You can then run any scripts that come with MCTDH as you like.

- In order to create a new project from scratch
- Click on Model Library -> My Models
- Click on + button on top left corner. Provide name and short description for your new project.
- Click on + button again in the next project screen and either create or upload an existing *.inp MCTDH input file.
- Click Settings -> Software and choose MCTDH from the dropdown menu.
- In the empty text box, type the name of the input script without the *.inp extension.
- Alternatively, you can type "xterm" in the empty text box to get a shell terminal with MCTDH access. You can then run any scripts that come with MCTDH as you like.

To see detailed step-by-step instructions on how to use MCTDH on Kogence free cloud supercomputing platform [click here].

## MCTDH Versions on Kogence

- Version 8.5.6.1
- Surfaces library is available
- POTFIT is available
- ANALYSE
- FILTER
- VCHAM
- MCTDH Scripts
- plspec plots the spectrum
- plauto plots the autocorrelation function,
- plnat plots the natural populations,
- plqdq plots the expectation values of the coordinates,
- plupdate, plupdate -e , and plspeed show information on the performance of the integration,
- plall prints a list of all pl-scripts

## References

## List of MCTDH Simulation Models on Kogence

Following are some related models available for cloning/copying by anyone: