Wavepacket Propagation¶
After constructing the vibronic Hamiltonian through the operator file, the next step in an MCTDH calculation is to propagate the nuclear wavepacket in time. Wavepacket propagation solves the time-dependent Schrödinger equation using the Hamiltonian defined in the operator file, allowing the evolution of the coupled electronic and vibrational degrees of freedom to be followed as a function of time.
Unlike conventional electronic structure calculations, which determine stationary energies and wavefunctions, wavepacket propagation provides direct access to the real-time dynamics of molecular systems. This enables the study of ultrafast photochemical processes such as electronic population transfer, nonadiabatic transitions, vibrational relaxation, and coherent nuclear motion.
Role of Wavepacket Propagation¶
The propagation calculation uses the Hamiltonian generated in the previous chapter together with an initial wavefunction to determine how the molecular quantum state evolves over time.
The overall workflow is
Electronic Structure Calculations
│
▼
Vibronic Hamiltonian
(Operator File)
│
▼
Wavepacket Input File
│
▼
MCTDH Propagation
│
▼
Time-dependent Wavefunction
│
▼
Population Dynamics
Expectation Values
Wavepacket Analysis
During propagation, MCTDH repeatedly evaluates the Hamiltonian and updates the wavefunction according to the chosen numerical integrator.
Input Files Required¶
A propagation calculation requires two primary input files.
-
Operator File (
.op)Contains the complete vibronic Hamiltonian, including
- vibrational frequencies,
- electronic state energies,
- linear vibronic coupling,
- quadratic vibronic coupling.
-
Propagation Input File (
.inp)Defines
- simulation parameters,
- primitive basis,
- multilayer tree,
- numerical integrator,
- initial wavefunction,
- propagation time.
Together, these files completely specify the quantum dynamics calculation.
Typical Workflow¶
A standard MCTDH propagation consists of the following stages.
- Read the operator file.
- Construct the primitive basis functions.
- Build the multilayer wavefunction tree.
- Generate the initial wavepacket.
- Solve the time-dependent Schrödinger equation.
- Save populations and wavefunction information at the requested time intervals.
The resulting output files can subsequently be analyzed to obtain electronic populations, vibrational dynamics, autocorrelation functions, spectra, and other time-dependent observables.
Example Used¶
Throughout this chapter, we use the propagation input file developed for the DTE-i-of model.
The calculation describes
- 4 diabatic electronic states
- 32 active vibrational modes
- Multilayer MCTDH wavefunction
- 300 fs propagation time
- Variable Mean Field (VMF) propagation
- Runge–Kutta fifth-order (RK5) integrator
This realistic example demonstrates the complete setup required for performing an MCTDH wavepacket propagation calculation.
Summary¶
Wavepacket propagation is the central step of an MCTDH calculation. Using the vibronic Hamiltonian generated in the previous chapter together with a user-defined propagation input file, MCTDH solves the time-dependent Schrödinger equation to simulate the quantum dynamics of coupled electronic and vibrational motion. The following sections explain each part of the propagation input file in detail, enabling users to construct, modify, and execute their own MCTDH dynamics simulations.