Dear fellow ADFlers,

a couple of weeks ago, I posted a question regarding the accuracy of the
ADF
numerical ZORA frequencies. I got a number of very interesting and
insightful
replies, and I would like to thank all of those who contributed. I felt
and feel
that I should summarize the responses to the list. However, I wanted to
try a
few of the suggestions first, hence the delay. (I am running serial ADF
only,
and this takes time.) I will start with my own observations and
comments, and
summarize/copy the original responses afterwards.

   Basically, I got the following comments and suggestions.
1) Imaginary modes of some 10 to 20i cm^-1 could well be an artefact of
the methods.
2) Based on that, it was suggested to boost the accuracy by
- using internal frequencies
- increasing the integration accuracy to 10
- tightening the convergence in the preceeding geometry optimization.
3) The imaginary modes could be correct, for instance due to
Jahn-Teller.
4) Suggestion to calculate the same case using another method (and
code) that has analytical second derivatives.
5) Serge Patchkovskii provided some very appropriate comments regarding
the approximate nature of the ZORA forces, see his reply below.
6) A related discussion appeared on the CCL recently.

   For my system, [(UO2(H2O)5]2+, D5 symmetry, I tried so far:

A) Comment (4) above of using another method and analytical
second derivatives. We have done that but it is tricky in the given
case:
the (symmetry of) the optimized geometry depends critically and
sensitively
on the level of basis set used in ECP calculations. I.e., changing from
6-31G*
to 6-31+G* (ligands) and at the same time uncontracting the U-ECP
basis set led to a change from 'nosym' to 'D5'. Thus, this doesn't
answer
the ADF specific question.
B) Internal coordinate frequencies, same accuracy (accint 8) and
structure as
before.
   One unrelated but interesting observation is that the symmetry is
NOT employed in this case, and ALL displacements are calculated. I do
not
see why this would be necessary but it is certainly rather expensive for
a
highly symmetric molecule. (Anybody from SCM listening???) For instance,

in my case, it is 25 cartesian geometries vs. 97 in the internal case, a
factor
of 4!
C) Boosting the integration accuracy to 10, but using the same structure

as before (geometry convergence set to
CONVERGE E=1e-4 GRAD=1e-3 RAD=1e-3;
INTEGRATION 6 6 6
during optimization); cartesian displacements.
   The result for both 'B)' and 'C)' is that the imaginary mode stays,
but
with a change in frequency fro 13i cm^-1 to 10i cm^-1. The next higher
mode changes from 83 to 75 cm^-1.
D) Optimization with much tighter criteria. This had quite an effect on
the
dihedral angle that is related to the modes of interest: it changes by
about
2.1 or so degrees. I have not yet done the frequencies on the new
structure -
I wanted to send out this summary at some point :-)

Finally, here is the summary of all the responses and my original
question.
I hope I did not forget anybody - my apologies if I did!

Best regards, Georg

==================================================
Original question:

Dear all,

in my calculated frequencies for a uranium containing closed-shell
molecule,
I get one imaginary frequency which is doubly degenerate due to
symmetry.
Now, while it is perfectly possible that these are 'real' because the
molecule
would have a lower symmetry in its ground state, I am still wondering
whether this is, in fact, noise, given that the calculated frequencies
are only
13.0i cm^-1.
   Thus, my questions are: What is the accuracy of the finite-difference
ADF
frequencies for very floppy modes? Can calculated frequencies of 13i
cm^-1
still be noise? Any further comments on the subject?
   I am using scalar ZORA, INTEGRATION 8, default values for
'frequencies',
PW91, frozen core ZORA basis V, cartesian coordinates, D5 symmetry.

==================================================

      Date: Thu, 15 Feb 2001 08:02:54 +0900
     From: "Luo Yi" <luoyi_at_aki.che.tohoku.ac.jp>

Dear Dr. Georg Schreckenbach:

About your question, you may try " INTEGRATION 10 " ,
Could you tell me how about your geometry
converge condition? You'd better increase the grad item.
Only comments for you, I whish you would tell me the result
from the advice at your convenience.

Best wishes

Mr. Yi Luo
Department of Materials Chemistry
Graduate School of Engineering, Tohoku University
Aoba-yama 07, Sendai 980-8579, Japan
Fax:+81-22-217-7235 Tel: +81-22-217-7237
E-mail: luoyi_at_aki.che.tohoku.ac.jp
             luoyi6_at_hotmail.com

==================================================

      Date: Thu, 15 Feb 2001 11:36:21 +0100
     From: Marcel Swart <m.swart_at_chem.rug.nl>

How large are the gradients ?
Because only in cases where the gradients are exactly zero,
are the lowest six eigenvalues exactly zero.
Normally we assume the gradient to be zero, when it is below
a certain threshold, which sometimes result in negative Hessian
eigenvalues.

                                           Marcel Swart
                     Theoretische Chemie (MSC) / Moleculaire Dynamica
(GBB)
                                    Rijksuniversiteit Groningen
                                            Nijenborgh 4
                                         9747 AG Groningen
                                           The Netherlands
                                        m.swart_at_chem.rug.nl
                                     http://go.to/m.swart

==================================================

Date: Thu, 15 Feb 2001 10:38:07 +0000
   From: Nik Kaltsoyannis <uccanka_at_ucl.ac.uk>

Georg,

> Thus, my questions are: What is the accuracy of the
finite-difference ADF
>frequencies for very floppy modes? Can calculated frequencies of 13i
cm^-1
>still be noise?

In my view, yes.

> Any further comments on the subject?

Sometimes if you change from cartesian to Z matrix displacements you can

eliminate very low frequency imaginary modes.

Cheers, Nik

==================================================

   Date: Thu, 15 Feb 2001 13:54:36 +0100 (CET)
   From: "Dr. Peter Burger" <chburger_at_aci.unizh.ch>

Dear Georg,

this discussion just showed up at CCL as well. I don't have
an answer as well but the same problem with Turbomole. Are
there plans for analytical frequencies in ADF?

Peter
------------------------------------------------
Peter Burger
University of Zuerich

==================================================

Date: Thu, 15 Feb 2001 09:07:44 -0500
   From: Jun Li <junli_at_chemistry.ohio-state.edu>

Dear Georg,

Happy Valentine ! The imaginary frequencies you got are so small that
it
might just be due to noise, as you suspected. I had similar problems
before. What I did was to increase the INTEGRATION from 6, to 8 and to
10.
It turns out that my small imaginary frequency goes from small imaginary
to
positive when using INTEGRATION=10. Therefore for floppy molecule you
probably need to use 10 and also a tight convergence criteria for
geometry
optimization (e.g. 1*10^-5), with a very tight convergence criteria
(10^-10) for SCF iteration as well.

Best regards,

Jun

P.S. I would check the low-frequency vibrational mode of a floppy
molecule
using a method that has analytical 1st- and 2nd-order energy
derivatives.

*******************************************************
Jun Li, PhD, Research Scientist
Department of Chemistry Tel: (614)292-5227 (Office)
The Ohio State University (614)529-7104 (Home)
100 West 18th Avenue Fax: (614)292-1685
Columbus, Ohio 43210-1173 E-Mail: li.208_at_osu.edu
USA
       Homepage: http://chemistry.ohio-state.edu/~junli
********************************************************

==================================================

Date: Thu, 15 Feb 2001 09:32:56 -0700 (MST)
   From: Serguei Patchkovskii <patchkov_at_ucalgary.ca>

Hi Georg,

As far as I know, ZORA gradients in ADF are
approximate to begin with, and do not correspond exactly to the Zora
Hamiltonian. This has to do with the derivatives of the Zora kinetic
energy, which are computed with _only_ the frozen core (or bare
nucleus) potential. This seems to work reasonably well for large
cores - but who knows what is going to happen once you take the
finite differences ....

I hope you'll send out a summary of the responces you get.

Regards,

/Serge.P

---
Home page: http://www.cobalt.chem.ucalgary.ca/ps/
Date:   Thu, 15 Feb 2001 10:53:24 -0700 (MST)
   From:     Serguei Patchkovskii <patchkov_at_ucalgary.ca>
On Thu, 15 Feb 2001, Georg Schreckenbach wrote:
> The funny thing is that this molecule, UO2(H2O)5_2+, is at some level
of
> basis set (in the ECP world) D5, and if you change the basis only
slightly,
> it is 'nosym'. I.e. the waters rotate almost freely. As one would
expect.
> So I only wanted to check that it is D5 at ZORA/ADF/V also, hence the
Well, I wouldn't necessarily trust ADF for this kind of problems - not
without doing a bit manual potential mapping along the sloppy mode. At
the very least, check the fit incompleteness corrections: ADF gradients
do not include those, and they turn out to be significant for floopy
modes (I had a case where the zero gradient point was almost 0.1A off
the minimum energy point along the floppy mode. The energy difference
was minuscle - like 0.2 kcal/mol - but it was a wrong stationaly point
all the same).
Cheers,
/Serge.P
---
Home page: http://www.cobalt.chem.ucalgary.ca/ps/
==================================================
   Date:     Thu, 15 Feb 2001 23:28:30 -0000
   From:     Mark Riley <riley_at_chemistry.uq.edu.au>
Hi,
Does your compound have a degenrate electronic state
at the D5 symmetry? If so your imaginary frequency may
be a jahn-teller active vibration.
cheer, Mark
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