CCL:G: Constrained optimization and frequency calculation

 Sent to CCL by: "Ankur Kumar Gupta" [ankkgupt||]
 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
 Thank you