I know Gaussian 16 can do it, but are there some free programs that can?

For simple excited state calculations using TD-DFT, we can use NWChem and Octopus. Can these do Franck-Condon factors?

  • 2
    $\begingroup$ +1 Are you asking about calculating vibronic spectra? Orca can do it. $\endgroup$
    – S R Maiti
    Commented May 8, 2021 at 8:17
  • 1
    $\begingroup$ +1 Welcome to our new community and thank you so much for contributing your question here!! We hope to see much more of you in the future!!! About this question: roughly how many atoms are there in your molecule? $\endgroup$ Commented May 8, 2021 at 16:53
  • $\begingroup$ We may need a little more detail on the systems you are working with to provide a recommendation. As hinted at by Nike, while there may be free software that can do this, it may not be possible (or at least very inefficient) to do for large systems. $\endgroup$
    – Tyberius
    Commented Jun 24, 2021 at 14:24

2 Answers 2



For a diatomic molecule, LEVEL can calculate all Franck-Condon factors (FKF):

$$ |\langle \psi_{v,J} | \psi_{v^\prime,J^\prime}\rangle|^2\tag{1}, $$

between rovibrational levels $(v,J)$ of one potential energy curve, and $(v^\prime,J^\prime)$ of another potential energy curve (or the same potential energy curve).

To calculate FKF, the variable LXPCT must be larger than 2 or smaller than -2, and the following can be treated as dummy variables MORDR, IRFN and DREF. If you set MORDR to be negative, you may experience faster computations.

This program was a project that Bob Le Roy worked on since the 1960s, and had contributions from several others over the decades, including myself. The latest version available online was from 2016, and since someone else needed a program like this for something else, I pushed the most recent version I could find into Github Here (let me know if you have any trouble compiling it).


  • Free and open-source.
  • Extremely accurate, and extremely fast (orders of magnitude faster and more black-box than other radial Schroedinger solvers I know some others have used).
  • Widely used and with a rich history spanning several decades.
  • There's not a lot of other programs available with this type of functionality.


  • Only works for diatomics.
  • You do need to get your accurate potential energy curve(s) from somewhere else (for example, you mentioned NWChem).
  • It's an "old school" program mainly with FORTRAN 77 style input and output, though it was probably originally written in FORTRAN 66, and we did modernize it over the years to use a lot of FORTRAN 90 (and beyond!) syntax.


FCBand is a Python package for simulating vibronic bands of electronic absorption spectroscopy using the Franck-Condon displaced harmonic oscillator (FC-DHO) models. These models are suitable for simulating the unresolved vibronic band shapes of electronic spectra that involve many electronic transitions and vibrational modes.



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