Summary: negative frequencies in MOPAC93

 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
 rosas-0at0-irisdav.chem.vt.edu                *  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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