CCL: Constrained optimization and frequency calculation

Gaussian by default assumes that the frequency analysis is done at a stationary point, and projects out the T+R to get 3N-6 frequencies.

If you are at a non-stationary point, use Freq=Projected to also project out the gradient, and thus get 3N-7 frequencies.

Note that this provides 3N-7 frequencies, regardless of the number of geometry constraints imposed, since the non-zero gradient is still only a one-dimensional quantity.




Frank Jensen

Assoc. Prof., Vice-Chair

Dept. of Chemistry

Aarhus University


From: |-at-| [ |-at-|] On Behalf Of Ankur Gupta ankkgupt**
Sent: 24. august 2016 20:00
To: Frank Jensen
Subject: CCL:G: Constrained optimization and frequency calculation



Thank you Prof. Dr. M. Swart for answering my question. I found Baker's paper really helpful. It discusses constrained optimization thoroughly but it does not focus much on normal mode analysis. I am more concerned about the frequencies that we get from the Hessian after constrained optimization. The algorithm for constrained optimization has been implemented in most of the computational chemistry software. But I am not able to understand the frequencies that it shows after the constrained optimization.

Thank you



On Sat, Aug 20, 2016 at 5:03 AM, Marcel Swart marcel.swart/./ <owner-chemistry[-]> wrote:

Dear Ankur,


I would suggest to have a look at PQS (Baker, Pulay and co-workers) or QUILD (Swart and co-workers).

Both use Baker’s elegant solution to constrained optimizations.


Baker, "Constrained optimization in delocalized internal coordinates”

Journal of Computational Chemistry 18, 1079 (1997)








On 19 Aug 2016, at 22:33, Ankur Kumar Gupta ankkgupt* <owner-chemistry*> wrote:


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 optimization.

Thank you

-= This is automatically added to each message by the mailing script =-
To recover the email address of the author of the message, please change
the strange characters on the top line to the * sign. You can also
look up the X-Original-From: line in the mail header.

E-mail to subscribers: CHEMISTRY* or use:

E-mail to administrators: CHEMISTRY-REQUEST* or use

Before posting, check wait time at:


Search Messages:



Prof. Dr. Marcel Swart, FRSC

ICREA Research Professor at
Institut de Química Computacional i Catàlisi (IQCC)
Univ. Girona (Spain)

COST Action CM1305 (ECOSTBio) chair
Girona Seminar 2016 organizer

IQCC director

RSC Advances associate editor

Young Academy of Europe member