Subject: DFT & freq. summary

From: "David Reichert" <[email-masked]>
Date: 27 Oct 1999 13:09:18 -0500

Hi,
I posted the following message awhile ago, and several people asked for a summary of the responses. I apologize for the delay in posting this. The orginal post was:

Hi,
I'm hoping that someone can provide some enlightenment. I've been running some DFT calculations on some copper - amine complexes which appear to end up having only C1 symmetry. In order to ensure that these are indeed minimum energy structures, I've run frequency calculations on them as well. My question is what should I really be seeing in the frequency calculations? I know that for a transition structure you look for one imaginary frequency, and that ideally the translational and rotational modes should drop out. But in real life with non-perfect calculations what do you want to see that says, "Yes, this is indeed a low energy fully converged struture". Any rules of thumb are more than welcome.

Following are the responses that I recieved. I'd like to thank everyone who responded for the additional info and helpful suggestions.
-Dave Reichert

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From: 	Brian Salter-Duke

	There are some real issues here. What code are you running? I'll comment
about G94. I have G98 on order.
	Ideally as you say you should have 6 frequencies that are close to zero
for the rotational and translational degrees of freedom. If you have a
local minimum all the others should be positive. If you have a transition
structure you should have one imaginary frequency which will appear as a
negative frequency.
	With RHF, MP2 etc. you get this. Particularly with opt=tight, you should get
the "zero" frequencies in +1 <-> -1. Many people are happy if they are in
+10 <-> -10 but I prefer to get them smaller.
	With DFT in G94 you are using a numerical grid that means the results are
not rotationally invarient - the results differ slightly if you rotate the
molecule in the cartesian frame. This means that the "zero" frequencies
are never really zero. The situation is worst for heavy atoms so with Cu
you will have more problems than with a straight 1st row organic molecule.
Using a larger grid improves the situation but increases the cost.
	My rule of thumb for Ga calculations is accept the results if the zero
frequencies are in +50 <-> -50 provided the smallest real frequency or
for a TS the negative frequency is well outside that range - e.g. 
more than 200 cm-1. If it is not well outside that range use a larger grid
and look at the changes in the frequencies etc. Always use opt=tight.
	It is a good idea to run two grids - the default and one slightly larger 
and compare the results. If the real frequencies and the TS negative 
frequency differ by less than 1 cm-1 you are probably OK.
	The rotational invariance problem is solved in the qchem code. I do not 
know about G98.

From: 	Robert Zellmer

	Of course your frequencies should all be positive if you have a
minimum.  Whether it's a global minimum is another story.  Depending on the
number of degrees of freedom, this could be an almost impossible thing to
determine.  However, you can try.
	One way is to use MM or semi-emp. methods to produce many low energy
conformations and then choice the most likely ones (lowest energy structures)
and run single point DFT calculations to see which one has the lowest energy.
This is something I'm doing now on several compounds.  One reason I've had to
do this is in running some AM1 calculations I got different optimized
structures from Gaussian98 and Spartan.  It can be a bit tedious and I know
people are working on the problem with global vs. local minima but I don't
recall that anyone has "solved" it.

From: 	Per-Ola Norrby

	Are you using Gaussian for this?  Because in that case, you always
get the output corresponding to a geometry optimization step, with four
criteria that have to be fullfilled.  If all of them say "YES", you're OK...
	Gaussian will also list the low frequencies twice.  The first list
is unprojected, in the second list the translations and rotations have been
projected out (that means that you won't see the 6 values closest to zero).
If you are at a stationary point, these should match closely (except for
the extra 6 in the first list), say within a few wavenumbers.  For a
minimum, all remaining vibrations should be positive.  If some are close to
zero, you  may have free rotations in your molecule.  If any of them are
below, say, 30-50 cm-1, you should treat thermodynamic contributions with
caution, because the harmonic approximation is no longer valid.

From: 	sergiusz kwasniewski

Hi,

for a fully optimized structure, you shouldn't have any imaginary (or
negative in case of gaussian freqs) frequencies left (or very small ones,
i.e. just a couple cm-1). The translational and rotational modes should be
dropping out here as well. A transition state (first order saddle point)
then has two imaginary freqs, a second order saddle point has three ...

I hope this is what you were looking for ...

From: 	Huub van Dam

	As you well know for a minimum energy geometry you should find all
positive frequencies. Furthermore my guess would be that all the
frequencies should come the same as with an exact calculation (i.e.
rotational and translational modes drop, modes across the minimum of a
well should have positive frequencies and modes across a maximum
imaginary frequencies). But in the case of DFT you would find deviations
due to the errors introduced by the numerical integration. I am not sure
about the accuracy one can achieve, but I think the errors should not be
larger than a few dozen wavenumbers. If it is more than either the
structure you found isn't what you where looking for either the
integration was to inaccurate and you should retry the calculation at a
higher precision.

From: 	Larry Cuffe

I dont think there are any hard and fast rules. For a
transition structure I prefer to see one negative frequency
preferrable  greater than 100cm/-1. If there are very low frequency
negatives around say -20 or -30 I dont worry about them. If there
is simething in between I try and visualize the movement involved
in the frequency and see what moving where. Generaly you can see
if this is the negative frequency of interest coresponding to the
sought for TS like this.  If you are using gaussian then gaussview
is usefull for visualizing negative modes. also in the achive entry
it gives the number of negative modes it feels are significant this
is the entry NIMAG=

From: 	Wilson, Bruce E

Ideally, what you want is to not see any imaginary frequencies in the
frequency calc.
However, we do DFT on organometallics, and no imaginary frequencies doesn't
always happen.
In general, I don't worry about imaginary frequencies below about 100 cm-1,
at least
not in terms of deciding that something is a local minimum instead of a
saddle 
point of some order.  A good minimizer, however, helps this immensely.
We've
almost never had problems with Jaguar (www.schrodinger.com).  If it
minimizes,
it seems to minimize to a true minimum, particularly if symmetry is turned
off.
It has also broken symmetry on several structures when it determined that it
needed to do so in order to get to a true minimum.

That's another rule of thumb I've followed.  If the output structure is C1
and
"looks reasonable", I don't worry about the frequency calc to verify the 
minimum.  The only times I run frequencies to verify a minimum is when
the final structure has some type of symmetry.

From: 	Michael Braunschweig

the nonexistance of imaginary frequencies is only one
criterion for a minimum. 
looking at the first derivatives of the energy you can see 
the forces that are used as convergence criteria from 
some programms (for example gaussian). if they are 
zero the geometry stay at an (global oder local) minumum.
also the last changes in energy or in the displacements
of the coordinates at the last optimization step are often
use as convergence criteria. but all these indicate both 
global and local minima at the energy hyper surface.
a minimum you have found in this way may also be 
a local one and not a fully converged structure. there 
are different methods for searching for a global 
minimum. try monte carlo or simulated annealing to 
examine different conformation.
____________________________________________
| David Reichert, Ph.D                     |
| Mallinckrodt Institute of Radiology      |
| Washington University School of Medicine |
| St. Louis, MO                            |
|                                          | 
| e-mail: [email-masked]      |
| voice: (314) 362-8461                    | 
| fax:   (314) 362-9940                    |
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