From owner-chemistry@ccl.net Fri Aug 19 18:01:00 2016 From: "Ankur Kumar Gupta ankkgupt*indiana.edu" To: CCL Subject: CCL:G: Constrained optimization and frequency calculation Message-Id: <-52350-160819163332-31517-nMtQtL5BDJZIvRZpUedtHQ * server.ccl.net> X-Original-From: "Ankur Kumar Gupta" 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