Subject: Summary: negative frequencies in MOPAC93

From: "Victor M. Rosas Garcia" <[email-masked]>
Date: Mon, 18 Sep 1995 21:29:02 -0400

Hi guys,

	Some time ago I posted a question about getting negative frequencies
using the COSMO model in MOPAC93.  If I delayed posting this summary, it was
because I wanted to understand better the problem and give a useful summary.
First of all, let me thank all those who responded:

Dr. J. J. P. Stewart.
Dr. Christopher J. Cramer
Dr. Frederic A. van Catledge

My original posting was:

*******************************************************************************
	It's me again :)  I've got a weird problem with MOPAC 93.  I trying to
calculate free energies of solvation for several sets of conformers (no TS's
involved).  This involves calculating the frequencies and principal moments of
inertia for each conformer, both in gas phase and in solution, to account for
the entropic contribution to the free energy.  I'm using FORCE for this, but
every now and then I get a *negative* frequency even though there are no
negative force constants in the force matrix.  The problem is more frequent
when I use FORCE and EPS=78.3, but it does appear for the gas phase
calculations too.  Usually there will appear one negative frequency with an
absolute value less than 40 cm^-1 (sometimes two).  FORCE found the gradients
to be acceptable (<2) in all cases so no additional minimization was done by
FORCE.
	According to the manual (regarding TS optimization) there is a way to
get rid of spurious negative frequencies which is to run a DRC along the
spurious mode.  However, when I use Cerius2 to animate the negative frequency
mode I see that it is quite complex.  Basically all the atoms move, so it is
not obvious to me how I can define a DRC along so many coordinates.
	BTW, the molecules I'm working on are either zwitterions or
 tetraalkylammonium cations (carnitine and choline).

	To make it brief my main questions are:
1) Is it possible to have a negative freq. and no negative force constant?
2) what meaning can be attached to a negative frequency (if any)?
3) Does it make sense to run FORCE and EPS=78.3 together?
4) Am I missing something really simple here?

Thanks in advance.

********************************************************************************

	Now, first of all, I have to make something clear.  In the original
posting, question number one was motivated by an error in reading MOPAC output:
 Basically I confused the FORCE MATRIX with the FORCE CONSTANT MATRIX.  It was
until later that I learned that the FORCE CONSTANT MATRIX is only printed when
using the keyword LARGE.  That's why I couldn't find any negative force
constants in the matrix but that weird thing motivated some nice replies from
some very cool people (names above).

	The answer to question number two is that those "negative" frequencies
are actually *imaginary* frequencies, just printed out as negatives as a way to
identify them.

	To question 3) the answer is: yes, it does make sense to use FORCE and
EPS=78.3, *but* you can get into a lot of trouble.  And the correction is not
easy.  Unfortunately I couldn't make it to the Chicago ACS meeting to hunt down
Dr. Stewart and/or Dr. Andreas Klamt and learn anything about this problem.

	I guess the answer to question 4) is NO.  I wasn't missing anything
really simple.

	Now, some interesting facts I learned about MOPAC93 (courtesy Dr.
Stewart):

>In MOPAC, the six trivial
>modes are explicitly calculated.  This calculation is trivially simple
>for the translations - for the `X' mode it is simply
>
>x 0 0 x 0 0 x 0 0 ...
>
>where x is 1/sqrt(n), with n being the number of atoms.  The rotation
>modes are more tricky - they involve the moments of inertia - but are
>not too difficult.  These six modes are projected out of the Hessian.

So there is never ambiguity in assigning the trivial modes, BUT the six trivial
modes are printed only if the keyword LARGE is used.

	To the suggestion that roundoff errors give rise to an artificial
negative frequency or that the Hessian is computed by a single-difference
approximation instead of a center-difference method.

>In MOPAC double sided derivatives are used.  If need be, quartic contamination
>can also be removed.
>
>(...) the step-sizes involved are (...) typically 1/60 Angstrom.

	Also, when one wants to get rid of an imaginary frequency one could try
running a reaction path calculation along the imaginary mode, but when a lot of
the atoms move it is difficult to choose the right reaction coordinate.  In
this case it's better to use the keywords DRC and IRC=n, where n is the number
of the mode one wants to get rid of.

	So, that's pretty much what I did: I started running series of reaction
paths and DRC's on each molecule that had the problem and in a good number of
cases that involved COSMO (I calculate approx. 80%) I got rid of the negative
frequencies that were bothering me. WARNING: it was a VERY tedious procedure.
 I think that the main problem was that the geometries were not completely
optimized, even though the energies varied very little.  I was consistently
getting the calculation stopped after the message

"HEAT OF FORMATION IS ESSENTIALLY STATIONARY"

which to me means that the potential energy surface is very flat, so there can
be somewhat significant changes in the geometry without really affecting the
energy.  I think that the negative frequencies were a manifestation of that
lack of geometric optimization (any other interpretations welcome). I don't
know if COSMO requires extreme precision in the location of the minimum, but it
could be (GNORM=0.01 didn't help because the message about the heat of
formation kind of overrides the GNORM).
	BTW, the negative frequencies showed up usually in very soft potential
modes, namely, carboxylate rotation, hydroxyl rotation and methyl rotation.

I hope this summary made sense, I'm a little tired after teaching the whole day
:(

-- 
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Victor M. Rosas Garcia                   * "How can we contrive to be 
[email-masked]                *  at once astonished at the  
Virginia Tech doesn't necessarily share  *  world and yet at home in it?"
the opinions you just read.	         *  G. K. Chesterton
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