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Generating the Absorption Spectrum

After the wavepacket propagation has completed, MCTDH generates the autocorrelation function of the propagated wavepacket. The absorption spectrum is obtained by taking the Fourier transform of this autocorrelation function.

MCTDH provides the utility autospec86, which performs this transformation and generates a spectrum that can be plotted using standard visualization software.

The workflow is

Wavepacket Propagation
          │
          ▼
Autocorrelation Function (auto)
          │
          ▼
      autospec86
          │
          ▼
     spectrum.pl
          │
          ▼
 Absorption Spectrum

Prerequisites

Before generating the spectrum, ensure that

  • the propagation has completed successfully,
  • the autocorrelation file (auto) is present in the working directory,
  • the autospec86 executable is available in your PATH.

For example,

/home/user/jitendra/dae/i-of-dynamics/wp3-pbf1-spf1/

contains

auto

which was generated during the propagation.

Running autospec86

The absorption spectrum is generated using

Generate the absorption spectrum

autospec86 2.5 4.5 ev 33 1

The arguments are

Argument Meaning
2.5 Lower energy limit (eV)
4.5 Upper energy limit (eV)
ev Energy unit
33 Exponential damping time (fs)
1 Damping order

After execution, MCTDH reads the autocorrelation function, performs the Fourier transform, and writes the calculated spectrum to a new file.

Program Output

A successful execution produces output similar to

autospec86 output

The inputfile is :

/home/user/jitendra/dae/i-of-dynamics/wp3-pbf1-spf1/auto

The outputfile is :

/home/user/jitendra/dae/i-of-dynamics/wp3-pbf1-spf1/spectrum.pl

No prefactor!

Emin, Emax :
2.500 4.500 eV

tau, iexp :
33.0 1

No. of plot-points :
1000

No. of t-points =
600

t-final =
600.000 fs

Moments:
M0 = 1.4185E-02
M1 = 3.1743E+00
M2 = 1.0466E+01

width = 6.2463E-01

Interpretation of the Output

Each quantity reported by autospec86 has a specific physical meaning.

Input File

inputfile : auto

This is the autocorrelation function generated during the MCTDH propagation.

Output File

outputfile : spectrum.pl

This file contains the calculated absorption spectrum.

It is an ASCII text file and can be plotted directly using Python, GNUplot, Origin, MATLAB, or other graphing software.

Energy Range

Emin = 2.5 eV

Emax = 4.5 eV

These values define the energy window over which the absorption spectrum is evaluated.

Only transitions lying within this interval are included in the generated spectrum.

Damping Parameter

tau = 33 fs

The finite propagation time introduces artificial oscillations in the Fourier transform. To reduce these truncation effects, the autocorrelation function is multiplied by a damping function before transformation.

The parameter

tau = 33 fs

controls the decay of this damping function.

Larger values preserve sharper spectral features, whereas smaller values produce smoother spectra with broader peaks.

Damping Order

iexp = 1

This parameter determines the functional form of the damping applied to the autocorrelation function.

For

iexp = 1

an exponential damping function is used.

Number of Plot Points

1000

The generated spectrum contains one thousand equally spaced energy points between the specified energy limits.

Increasing this number produces a smoother plotted curve but does not increase the physical resolution of the spectrum.

Propagation Length

No. of t-points = 600

t-final = 600 fs

These values indicate that the Fourier transform uses

  • 600 autocorrelation points,
  • corresponding to a total propagation time of 600 fs.

The maximum propagation time determines the achievable spectral resolution.

Spectral Moments

The program also reports

M0

M1

M2

width

These correspond to the statistical moments of the spectrum.

Quantity Meaning
M0 Total spectral intensity (area under the spectrum)
M1 First spectral moment (mean transition energy)
M2 Second spectral moment
width Root-mean-square spectral width

These quantities provide a compact description of the calculated absorption spectrum and are useful for comparing different simulations.

The Generated Spectrum File

After the calculation, the file

spectrum.pl

is created.

The beginning of the file looks like

Beginning of spectrum.pl

# Energy[ev]                  g0               g1               g2             g5 (g'1)

2.50000000E+00    1.07254956E+00    1.07265249E+00    1.07275469E+00    1.07294543E+00

2.50200000E+00    1.06060898E+00    1.06068017E+00    1.06075236E+00    1.06089647E+00

2.50400000E+00    1.04886099E+00    1.04890311E+00    1.04894725E+00    1.04904640E+00

The first column contains the transition energy in electron volts.

The remaining columns contain the absorption intensity calculated using different damping functions provided by autospec86.

For most applications, the g0 column is used to construct the absorption spectrum, while the remaining columns provide alternative broadenings for comparison.

Summary

The autospec86 utility converts the autocorrelation function generated during the MCTDH propagation into an absorption spectrum by performing a Fourier transform. The resulting spectrum.pl file contains the transition energies and corresponding spectral intensities, providing the numerical data required to visualize and analyze the simulated absorption spectrum. In the next section, we will use this file to generate publication-quality absorption spectra and discuss how to interpret the resulting peaks.