Tuesday 1998 August 11
 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           .   .
                 -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?
               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).
                   3-AUG-1998 17:36:45.52
 >From:  IN%"peon' at \`"  "Per-Ola Norrby"
 To:     IN%"elewars' at \`"  "E.
         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).
         Per-Ola Norrby
 Per-Ola Norrby, peon' at \`
 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%"r40757' at \`"  "Anatoli Korkin"
 To:     IN%"elewars' at \`"  "E.
 Lewars", IN%"chemistry' at \`infome"  "chemistry' at \`", IN%"bartlett'
 at \`"  "Rod
 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
 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.
 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: r40757' at \`
 X-Sender: sabrash' at \`
 Dear Professor Lewars,
         I cannot give you the answer for the theoretical case, but can explain t
 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
 sabrash' at \`
 "I believe in the open mind, but not so open your brain falls out."
 Subject: neg. E act
 To: elewars' at \`
 Date: Mon, 3 Aug 1998 15:10:42 -0500 (EDT)
 X-Mailer: ELM [version 2.4 PL20]
 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
 villa' at \`
 -What you call "activation energy" is, in fact, an energy barrier.
 Activation energy is a kinetic concept that comes from the Arrhenius
 -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
 -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
           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: elewars' at \`
 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
 Luke Anthony Burke              tel:609-225-6158 (-6142)
 Professor and Chair,            fax:609-225-6506
 Rutgers University              burke' at \`
 Camden, NJ 08102, USA 
 Alan Shusterman
 Date: 03 Aug 98 13:42:35 PDT
 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 Shusterman
 Department of Chemistry
 Reed College
 Portland, OR
            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" <elewars' at \`>
 > 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.