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MCTDH

MCTDH (Multi-Configuration Time-Dependent Hartree) is a powerful quantum dynamics package for solving the time-dependent Schrödinger equation of multidimensional molecular systems. It enables accurate simulations of nuclear wavepacket dynamics, nonadiabatic transitions, vibrational motion, and photochemical processes while efficiently treating systems with many degrees of freedom.

Unlike electronic structure packages such as Gaussian, GAMESS, or ORCA, which compute electronic energies and molecular properties, MCTDH focuses on the time evolution of nuclear wavepackets on one or more potential energy surfaces.

In this documentation, we demonstrate the complete workflow required to perform an MCTDH simulation, beginning with the generation of operator files, followed by wavepacket propagation, and finally the diagonalization of the Hamiltonian to obtain stationary vibrational eigenstates.

Official Resources

  • MCTDH Documentation

    Official user manual describing the input structure, algorithms, operator definitions, and available propagation methods.

    MCTDH Documentation

  • MCTDH Website

    Official website containing installation instructions, downloads, tutorials, and publications.

    Visit Website

  • MCTDH Publications

    Foundational papers describing the theoretical background and numerical implementation of the MCTDH method.

    Learn More

Recommended Learning Workflow

If you are new to MCTDH, we recommend following the tutorials in the order shown below.

┌────────────────────────────┐
│ Operator File Generation   │
└─────────────┬──────────────┘
              ▼
┌────────────────────────────┐
│ Wavepacket Propagation     │
└─────────────┬──────────────┘
              ▼
┌────────────────────────────┐
│ Hamiltonian Diagonalization│
└────────────────────────────┘

Each tutorial introduces one essential stage of an MCTDH calculation.

  • Operator File Generation explains how Hamiltonians, potential energy surfaces, kinetic energy operators, and coupling terms are assembled into an operator file.
  • Wavepacket Propagation demonstrates the time evolution of an initial nuclear wavepacket using the MCTDH propagation algorithms.
  • Hamiltonian Diagonalization computes vibrational eigenvalues and eigenfunctions by diagonalizing the Hamiltonian represented in the MCTDH basis.

Tutorials

  • Operator File Generation

    Learn how to construct MCTDH operator files containing kinetic energy operators, potential energy surfaces, and electronic couplings.

    Explore Operator Generation

  • Wavepacket Propagation

    Perform time-dependent propagation of nuclear wavepackets and analyze their evolution on coupled potential energy surfaces.

    Explore Wavepacket Propagation

  • Hamiltonian Diagonalization

    Obtain stationary vibrational eigenstates and eigenenergies through Hamiltonian diagonalization within the MCTDH framework.

    Explore Diagonalization

Future Tutorials

The following topics will be included in future updates of the MCTDH documentation.

  • Primitive Basis Construction

    Selection of DVRs, basis functions, and mode combinations for multidimensional calculations.

  • Potential Energy Surface Fitting

    Construction and fitting of PES representations suitable for MCTDH simulations.

  • Multi-State Dynamics

    Simulations involving multiple coupled electronic states and nonadiabatic transitions.

  • Expectation Values

    Calculation of populations, expectation values, autocorrelation functions, and spectra from propagated wavepackets.

  • Wavepacket Visualization

    Visualization of wavepacket motion, probability densities, and time-dependent observables.

  • Improved Relaxation

    Determination of ground and excited vibrational states using the improved relaxation algorithm.