CCL:G: Constrained optimization and frequency calculation

Dr. Jensen,
 Apologies for the pedantry, but is "one-dimensional quantity" the
 proper
 term?  Wouldn't, say, "order-one tensor quantity" be more accurate?
 That is to say, the gradient and each of the normal modes are individually
 3N-dimensional, order-one tensor quantities, are they not?
 Best regards,
 Brian
 On Wed, Aug 24, 2016 at 3:27 PM, Frank Jensen frj===chem.au.dk <
 owner-chemistry+/-ccl.net> wrote:
 > 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
 >
 >
 >
 > Frank Jensen
 >
 > Assoc. Prof., Vice-Chair
 >
 > Dept. of Chemistry
 >
 > Aarhus University
 >
 > http://old.chem.au.dk/~frj
 >
 >
 >
 > *From:* owner-chemistry+frj==chem.au.dk+/-ccl.net [mailto:
 > owner-chemistry+frj==chem.au.dk+/-ccl.net] *On Behalf Of *Ankur Gupta
 > ankkgupt**umail.iu.edu
 > *Sent:* 24. august 2016 20:00
 > *To:* Frank Jensen
 > *Subject:* CCL:G: Constrained optimization and frequency calculation
 >
 >
 >
 > Hello,
 >
 > 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
 >
 > Ankur
 >
 >
 >
 > On Sat, Aug 20, 2016 at 5:03 AM, Marcel Swart marcel.swart/./icrea.cat <
 > owner-chemistry[-]ccl.net> 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)
 >
 > http://dx.doi.org/10.1002/(SICI)1096-987X(199706)18:8%
 > 3C1079::AID-JCC12%3E3.0.CO;2-8
 >
 >
 >
 > PQS:
 >
 > http://www.pqs-chem.com/capabilities.php
 >
 >
 >
 > QUILD:
 >
 > http://www.marcelswart.eu/quild
 >
 > https://www.scm.com/documentation/Quild/index/index
 >
 >
 >
 > Marcel
 >
 >
 >
 > On 19 Aug 2016, at 22:33, Ankur Kumar Gupta ankkgupt*indiana.edu <
 > owner-chemistry*ccl.net> wrote:
 >
 >
 >
 >
 > 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
 >
 >
 >
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 >
 > _____________________________________
 > 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
 >
 >
 >
 > web
 > http://www.marcelswart.eu
 > vCard
 > addressbook://www.marcelswart.eu/MSwart.vcf
 >
 >
 >
 >
 >
 >
 >
 >