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Propagation Input File

The propagation input file controls every aspect of an MCTDH wavepacket propagation calculation. While the operator file defines the vibronic Hamiltonian, the propagation input specifies how the Hamiltonian should be used during the time evolution of the wavepacket.

It contains information about

  • the simulation time,
  • memory allocation,
  • the operator file to be used,
  • primitive basis functions,
  • multilayer tree structure,
  • numerical integrator,
  • and the initial wavefunction.

Together with the operator file, this input completely defines the MCTDH propagation calculation.

Overall Structure

The propagation input is organized into several sections.

Snippet 1 — Overall Structure

RUN-SECTION

ALLOC-SECTION

OPERATOR-SECTION

PRIMITIVE-BASIS-SECTION

ML-Basis-Section

INTEGRATOR-SECTION

INIT_WF-SECTION

Each section controls a different aspect of the propagation and is discussed below.

RUN-SECTION

The RUN-SECTION contains the general information about the propagation, including the job name, propagation time, and output frequency.

Snippet 2 — RUN-SECTION

RUN-SECTION
  name = wp3-pbf1-spf1
  propagate
  title = DTE-i-of with 4 states and 32 modes
  steps auto gridpop=el
  tinit=0.0  tfinal=300.0  tout=0.5
end-run-section

Explanation

Keyword Description
name Name of the calculation.
propagate Performs a time-dependent propagation.
title User-defined description of the calculation.
steps auto MCTDH automatically determines the required number of integration steps.
gridpop=el Prints electronic populations during propagation.
tinit Initial propagation time (fs).
tfinal Final propagation time (fs).
tout Time interval between printed outputs (fs).

For this calculation, the wavepacket is propagated from 0 fs to 300 fs, and observables are written every 0.5 fs.

ALLOC-SECTION

The allocation section reserves memory for different MCTDH objects.

Snippet 3 — ALLOC-SECTION

ALLOC-SECTION
   maxpar=800
   maxham=33
   maxmuld=33
end-alloc-section

Explanation

Keyword Description
maxpar Maximum number of parameters allowed in the operator file.
maxham Maximum number of Hamiltonian terms.
maxmuld Maximum multilayer dimensions.

These values depend on the size and complexity of the Hamiltonian.

OPERATOR-SECTION

This section specifies which operator file should be used.

Snippet 4 — OPERATOR-SECTION

OPERATOR-SECTION
opname = i-of
end-operator-section

The keyword

opname = i-of

instructs MCTDH to read the Hamiltonian from the operator file

i-of.op

generated in the previous chapter.

PRIMITIVE-BASIS-SECTION

The primitive basis defines the basis functions used to represent each vibrational degree of freedom.

Snippet 5 — Primitive Basis

PRIMITIVE-BASIS-SECTION
v1   HO   26  0.00  1.0  1.0
v2   HO   32  0.00  1.0  1.0
v3   HO   65  0.00  1.0  1.0
...
v32  HO   22  0.00  1.0  1.0
el   el    4
end-primitive-basis-section

Each line has the form

Mode   Basis   Grid Size   Shift   Scale   Mass

For example,

v3 HO 65 0.00 1.0 1.0

means

  • Mode 3
  • Harmonic Oscillator basis (HO)
  • 65 primitive basis functions
  • Zero coordinate shift
  • Unit scaling
  • Unit mass weighting

The last line

el el 4

defines the electronic degree of freedom.

ML-Basis-Section

The multilayer basis section specifies how the wavefunction is decomposed into the multilayer tree used by ML-MCTDH.

Snippet 6 — ML Tree

ML-Basis-Section

0> 4 4
 1> 16 16
     2> 8 8
         ...
     4> [v3 v24 v16 v19]
     4> [v32 v22 v8 v12]
     ...

 1> [el]

end-ML-Basis-Section

The numbers

0>
1>
2>
3>
4>

represent successive layers of the tree.

The square brackets define the vibrational modes grouped together within each branch.

For example,

[v3 v24 v16 v19]

indicates that these four vibrational modes are treated together in one branch of the multilayer tree.

The final line

[el]

places the electronic degree of freedom in a separate branch.

INTEGRATOR-SECTION

This section determines the numerical propagation algorithm.

Snippet 7 — Integrator

INTEGRATOR-SECTION
VMF
RK5 = 1.0d-7, 2.0d-4
end-integrator-section

Explanation

VMF

: Variable Mean Field propagation scheme.

RK5

: Fifth-order Runge–Kutta integrator.

The two numerical values specify the error tolerances used for adaptive time stepping.

INIT_WF-SECTION

This section defines the initial wavefunction.

Snippet 8 — Initial Wavefunction

INIT_WF-SECTION

build

init_state = 3

v1  eigenf h1
v2  eigenf h2
...
v32 eigenf h32

end-build
end-init_wf-section

Initial Electronic State

init_state = 3

indicates that the propagation begins on electronic state 3, corresponding to the photoexcited electronic state used in this study.

Vibrational Wavefunction

Each vibrational mode is initialized in the harmonic oscillator eigenfunction associated with that mode.

For example,

v7 eigenf h7

means that vibrational mode 7 is initialized in its harmonic oscillator eigenstate.

The complete initial wavefunction is therefore constructed as a direct product of harmonic oscillator eigenfunctions together with the selected electronic state.

End of Input

The propagation input concludes with

Snippet 9 — End of File

end-input

which signals the end of the MCTDH input file.

Summary

The propagation input file defines every aspect of the MCTDH simulation. The RUN-SECTION specifies the propagation time, the ALLOC-SECTION reserves memory, the OPERATOR-SECTION links the Hamiltonian, the PRIMITIVE-BASIS-SECTION defines the harmonic oscillator basis, the ML-Basis-Section constructs the multilayer tree, the INTEGRATOR-SECTION selects the numerical propagation algorithm, and the INIT_WF-SECTION specifies the initial quantum state. Together, these sections provide all the information required to perform an MCTDH wavepacket propagation calculation.