Subject: NEG ACTIV E: SUMMARY

From: "E. Lewars" <[email-masked]>
Date: Tue, 11 Aug 1998 13:32:26 -0400 (EDT)

Tuesday 1998 August 11

Hello,

Thanks to all who replied to my question about negative activation energies:
P-O Norby, A. Korkin, S. Abrash, M. Hohmann, J. Vill'ai Fre, l. Burke,
A. Shusterman and J. Perry (I hope I haven't missed any one).

The question was:

Sometimes one gets a _negative_ value for an activation E.  For example

                  O               O
                   \\              \\...
                    C---O           C---O
                    |   |  ----->   .   . transition state   --> CO2 + N2
                    N===N           .   .
                                    .....
                                    N====N
                -297.56194 h
                                     -297.56281 h

      activ E = -0.00087 h = -2.28 kJ/mol     G2(MP2) energies

 Sometimes one gets a negative value with and without the ZPE corection.

 Is there any special theoretical significance to such "impossible"
activation E's?  Or can one just say that (since not much below zero) they
are compatible with a low positive barrier?

     Thanks

              E. Lewars
==============

I now see that -ve activation E's can easily be obtained if the barrier is low;
they are essentially just errors caused by errors in the ZPE, or, in the case
of single-point calcs on a structure optimized at a lower level (which is
what G2-type calcs are), errors can arise from the fact that the lower-level
statonary points will not be exactly the max and min on the higher-level PES.
                    .
                  .   .
      .         .x      .                     x
        .     .  |       .                    |
          .. .   |        . .~.               | -ve       ~
        .        |       . ./|\ .             |          /|\
         .      \|/    .    .|    .          \|/          |
           .     ----------- x      .         x           |  +ve
              .     .        |.       .                   |
                . .  ________|_.        .                 |
                 ~              .                         ~
                                 .

 I think this is the cause in this case; as others pointed out (SUMMARY BELOW),
there can be other causes of neg activ E's, like precomplexation (van der Waals
complexes) and etc (J Chem Phys, 1997, 107, 7266), and when the
Arrhenius A factor dominates the exponential factor (deltaE ~- 0).

------------
SUMMARY OF RESPONSES:

                  3-AUG-1998 17:36:45.52
>From:  IN%"[email-masked]"  "Per-Ola Norrby"
To:     IN%"[email-masked]"  "E. Lewars"
Subj:   CCL:NEGATIVE ACTIVATION E's

        Well, in this case, it just means you use an improper method...
The G2 methods are extrapolation methods that depend on the geometry being
well represented by a low level method.  In this case, you are using
HF/6-31G* to locate the TS geometry, I guess this is the source of your
problem.  If you use a method where you calculate the energy at the same
level as your geometry, this type of problem should disappear (there are
other possible sources of apparent negative TS energies, like
precomplexing, but that should not apply in your case).  For some good
possible choices for geometry optimization levels, I'd suggest
MP2/6-311G**, or B3LYP/6-31G* (depending on your computational resources
and/or theological leaning).

        The G2 methods were developed to calculate VERY accurate heats of
formation, but in general, I wouldn't recommend them for TS calculations
(just a personal opinion, I'd like to hear if there is a concensus on this).

        Regards,

        Per-Ola Norrby

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Per-Ola Norrby, [email-masked]
Royal Danish School of Pharmacy, Dept. of Med. Chem.
Universitetsparken 2, DK-2100 Copenhagen, Denmark
Tel: +45-35376777-506, +45-35370850, fax +45-35372209
=============

>From:  IN%"[email-masked]"  "Anatoli Korkin"
To:     IN%"[email-masked]"  "E. Lewars", IN%"chemistry@infome
ister.ccl.net"  "[email-masked]", IN%"[email-masked]"  "Rod
 Bartlett"
Subj:   CCL:NEGATIVE ACTIVATION E's

Negative activition energies you may get in two cases (may be someone
knows more): 1) There is an intermediate complex between reagents and 
a TS. In this case everything is "normal". Some SN2 gas phase 
reactions have "negative" activitations energies. This led first to a
suspecion among experimentalists, who studied these reactions in
solutions,
that theory was wrong, but later this result has been confirmed for
gas phase reactions. 2) For very low barriers you may get negative
activation energies, if you do (higher level) single point calculations
using geometries optimized at another (lower correlation) approach.
If you optimize a TS and reagents at the same level and there is
no an intemediate mimimum on a reaction pathway you should not get
your electronic energy for TS lower than that one for reagents. Of
course, zero point energy correction may change the sign of the barrier,
if it is very small (e.g. 1 kcal/mol or lower). Anyway at such low
barriers a conventional transition state theory is hardly applicable,
and a dynamical treatment is required.

Regards,

Anatoli

P.S. We have a paper on CN2O2 species including the complex below.
An activation energy we got at CCSD(T)/TZP//MBPT(3)/6-31G* was 0.5
kcal/mol before and -0.3 kcal/mol after ZPE correction.
-----------

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

Anatoli A. Korkin, Ph.D         Predictive Engineering Lab
Computational Chemist           Semiconductor Products Sector
Motorola Inc., MD M360          Tel:    (602) 655-3171
2200 W. Broadway Road           Fax:    (602) 655-5013
Mesa AZ 85202                   E.mail: [email-masked]
                                        
*******************************************************************

X-Sender: [email-masked]
Subject: Re: CCL:NEGATIVE ACTIVATION E's

Dear Professor Lewars,
        I cannot give you the answer for the theoretical case, but can explain t
he
significance for experimentally determined negative activation energies.

The rate constant for a reaction in the Arrhenius model is given by k =
A(T) exp (-Ea/RT).  Because the activation energy temperature dependence
typically swamps that due to the preexponential factor, typical Arrhenius
analyses ignore the temperature dependence of the A term.  However when Ea
is for all practical purposes zero, then the temperature dependence is that
of the A factor which tends to increase with decreasing temperature.  This
therefore appears as a negative activation energy.  Such reactions are
better fit by the equation

  k = AT^m exp(-E0/RT), where E0 is equivalent to the zero k activation energy.

Best regards, 

Sam Abrash

>==============
Sam Abrash
Associate Professor
Department of Chemistry
University of Richmond
Richmond, VA  23174
(804) 289-8248
Fax: (804)289-8482
[email-masked]

"I believe in the open mind, but not so open your brain falls out."
==================

Subject: neg. E act
To: [email-masked]
Date: Mon, 3 Aug 1998 15:10:42 -0500 (EDT)
X-Mailer: ELM [version 2.4 PL20]

Hi!

Negative activation energies can result
- from ZPE corrections or
- if you derive your relative energies from single point calculations
  and the geometries used are not good enough (i.e. the geometries at the
  level of opt and at the level of single points deviate considerably) 

If you get a "neg. activation energy" at the level of geometry opt., 
something is wrong. I suggest to look at the vector of the imaginary frequency 
first. If it seems to be ok check the transition state with
an IRC (intrinsic reaction coordinate) calculation. 

Good luck,
Matthias       M. Hohmann
============

Jordi Villa i Freixa
Department of Chemistry
University of Southern California
Los Angeles, CA, USA, 90089-1062 
Tlf: 1-(213)-740 7671 Fax: 1-(213)-740 2701
[email-masked]      http://t1.chem.umn.edu/~villa

-What you call "activation energy" is, in fact, an energy barrier. 
Activation energy is a kinetic concept that comes from the Arrhenius 
equation.

-Probably the small negative value you obtain is due to the G2 method,
where you are not exploring exactly a concrete potential energy surface, 
but adding the contributions of several corrections to the initial energy 
surface. 

-The example you are posting is really interesting because of the low 
barrier (in your case is negative, but I guess that using only the
non-G2-corrected surface the barrier would be positive or zero). This 
means that considering the barrier to be the given value could lend you 
to an error when trying to understand kinetic experimental results, for 
example. The location of only the saddle point on this reaction will not 
be enough to understand the dynamics of the system, and a treatment with 
variational transition state theory could be necessary.

If you want more information about the dynamic treatment of this kind of 
barrierless or almost barrierless reactions take a look to:

J. Chem. Phys. 1997, 107, 7266
J. Am. Chem. Soc. 1998, 120, 5559.

I hope this will help

Yours

Jordi
===========

          Aug 3  Luke A. Burke      (31)   impos tsCommand: Read MessageMessage 5/17 from Luke A. Burke                           Aug 3 '98 at 6:59 pm

Date: Mon, 3 Aug 1998 18:59:03 -0400
X-Mailer: Z-Mail (3.2.3 08feb96 MediaMail)
To: [email-masked]
Subject: impos ts
Mime-Version: 1.0

 ...............

If your structure is indeed a ts, then there must be a minimum and another ts
between your drawn structures. You did not give the geometry of the ts but I
suspect that there is the involvement of van der Waals complexes.
BTW, in the history of ts oddities, I found a reaction (rotation) where the Ea
>0, but Ha<0 and Ga<0.

Salut, de koste en de wind van achter, en de steenweg tot huis toe (plat
Leuvense)

Luke

-- 
Luke Anthony Burke              tel:609-225-6158 (-6142)
Professor and Chair,            fax:609-225-6506
Rutgers University              [email-masked]
Camden, NJ 08102, USA           http://camchem.rutgers.edu/~burke
==============

Alan Shusterman
Date: 03 Aug 98 13:42:35 PDT
Subject: Re: CCL:NEGATIVE ACTIVATION E's

I noticed that your negative barrier results from comparison of =
G2(MP2) energies. I'm not very familiar with the G2 model, but I =
was wondering what model was used to identify the reactant minimum =
and transition state, and did this model give a negative or =
positive barrier?

Alan
----------------
Alan Shusterman
Department of Chemistry
Reed College
Portland, OR
www.reed.edu/~alan
==============================

           Aug 3  Jason K. Perry     (31)   Re:  CCL:NEGATIVE ACTIVATION E'sCommand: Read MessageMessage 8/17 from Jason K. Perry                          Aug 3 '98 at 1:53 pm

Date: Mon, 3 Aug 1998 13:53:36 -0700 (PDT)
To: "E. Lewars" <[email-masked]>
Subject: Re:  CCL:NEGATIVE ACTIVATION E's

> Sometimes one gets a negative value with and without the ZPE corection.

The reason you're seeing negative activation energies is because with the
G2 method you are calculating the geometry at one level and reporting
an energy at a different level.  At the level that the geometry was
determined it is most certainly the case that the activation barrier
is positive.  For example, if I calculate geometries for reactant, product
and transition state at the HF/6-31G** level, the transition state will
be correct for that level and show a positive barrier.  If I then do
single point B3LYP/6-31G** calculations using those HF/6-31G** geometries
the transition state will not be correct for the new level, and
thus there is no guarantee that the barrier will be positive.

        Jason Perry
        First Principles Research, Inc.
================