# CCL:G: Constrained optimization and frequency calculation

*From*: "Ankur Kumar Gupta"
<ankkgupt[]indiana.edu>
*Subject*: CCL:G: Constrained optimization and frequency
calculation
*Date*: Fri, 19 Aug 2016 16:33:31 -0400

Sent to CCL by: "Ankur Kumar Gupta" [ankkgupt||indiana.edu]
Hello,
I have been reading about constrained optimization. I have read several papers
related to the topic including the classic Reaction path Hamiltonian for
polyatomic molecules by Miller et al. This and other research articles describe
what is known as 'projection operator' method to do optimization keeping one or
more internal coordinates constant. Theoretically, we should get 3N-6 non-zero
eigenvalues from the force constant matrix (for a molecule having N nuclei) but
if we apply m number of constraints in the molecule, we should obtain 3N-6-m
non-zero eigenvalues (frequencies). Also, in cases where the constraint
corresponds to a non-equilibrium geometry, there will be coupling between
rotational and vibrational motion due to which the number of non-zero
eigenvalues might change. But for the sake of simplicity, we can talk about
equilibrium geometries only. I use Gaussian 09 and I observed that the number of
non-zero eigenvalues did not change after constrained optimization. I know there
are many computational chemistry softwares out there and I would like to know if
there is a software which can do constrained optimization correctly and give me
the right number and magnitude of eigenvalues (frequencies) after the
optimization.
Thank you
Ankur