From chemistry-request@server.ccl.net Fri Jun 30 20:14:56 2000 Received: from smtppop3.gte.net (smtppop3pub.gte.net [206.46.170.22]) by server.ccl.net (8.8.7/8.8.7) with ESMTP id UAA02845 for ; Fri, 30 Jun 2000 20:14:55 -0400 Received: from oemcomputer (1Cust183.tnt6.bos2.da.uu.net [63.22.117.183]) by smtppop3.gte.net with SMTP for ; id TAA8652835 Fri, 30 Jun 2000 19:12:16 -0500 (CDT) Message-ID: <005901bfe2f0$63058dc0$67e6fea9@oemcomputer> From: "David Anick" To: Subject: Summary: Activation Barrier Date: Fri, 30 Jun 2000 20:07:38 -0400 Dear CCL subscribers, Here is a summary of the five responses to the inquiry I posted recently about interpreting an apparently negative activation barrier. Thanks to all who responded. I don't believe a consensus arose, but I hope the discussion continues and is ultimately found to be fruitful. Since some of you asked, I have examples where the effect in (1) occurs for situations computed at the MP2/6-311++g** level of accuracy. David J. Anick MD PhD First, the query: > I would be interested in opinions, examples, best guesses, > references, or published data related to the following two > questions. I will be happy to summarize responses. > (1) I have a unimolecular "rearrangement" reaction for which I > have computed state A ("reactant"), state B ("product"), and > the T-state. All three are converged to nicely by optimization > programs, with A and B being PES minima and the TS a 1st order > saddle. The electronic energy of A is below that of the TS by > 3 kcal/mol, but when I compute and add in the ZPE's, state A > has slightly higher energy than the TS (by ~ 0.2 kcal/mol). > State B is of considerably lower energy than either, even after > ZPE corrections. > What does this mean? Would the molecule quickly tunnel > out of state A at 0 K? Can I consider A to be a stable (even > if short-lived) state of the molecule, or must it be viewed as > an unstable intermediate or transitional state? Would it be > correct to use the energy difference between A and B, to talk > about a Boltzmann distribution of a population into states > A and B, or would it all be basically B? > (2) Like (1) in that there is a unimolecular reaction A -> B, > but now both A and B have energies below the TS (including > the ZPE corrections). My question is, is there a ball park > estimate for the temperature T at which A becomes unstable, > in terms of the activation barrier (i.e. DG = G(TS) - G(A)). > I'm open to opinions about how "unstable" should be defined, but > an operational definition could be "half-life of A less than > a minute". I think this comes down to predicting the pre- > Arrhenius factor, and there will be a wide range answers > depending on the reaction, but I wonder if anyone can offer > gross generalizations, e.g. "small organic molecules for which > such a rearrangement pathway exists, are typically unstable > above temp DG/10kB", or the like. The DG's (with ZPE included) > I'm looking at are between 2 and 10 kcal/mol, and the reactions > involve the movement of 3 to 6 second row atoms. ---------------------------------------------------------------- RESPONSE 1: (Alan Shusterman Chem Dept Reed College Portland, OR 97202) This is a good "can of worms". I'm not sure what the right answer is, so I'll give you my guess/opinion. There are a couple of ways that I might regard this situation: If I insist on using the Born-Oppenheimer approximation AND I believe that the ZPE calcs are accurate, then A is not a minimum and T is not a transition state. All of the molecules will be in B (no A=B equilibrium). I might wonder if the ZPE calcs are right, however. They often make some kind of assumption about the shape of the surface near the minimum, i.e., typically they assume a quadratic surface and a molecule that acts like a harmonic oscillator. If these assumptions are inappropriate then maybe A will turn out to be a minimum after all. One of the other hand, maybe the ZPE results are right. Then one might question the use of the Born-Oppenheimer approximation for this part of the PES, i.e., electron and nuclear motion may be coupled significantly for geometries near A and T. Of course, there is also another problem...perhaps at a higher level of theory, the shape of the surface will be different. As for your second question, again I'm no expert, but organic chemists have a time-honored tradition to rely on...we assume the pre-Arrhenius factors for unimolecular reactions to be in the range 1e12 to 1e14 per second. ---------------------------------------------------------------- RESPONSE 2: (E. Lewars) When the TS is only slightly above a reactant (a few kJ or less), adding the ZPE can put the TS below one (or both) reactants, especially if the ZPE was calculated >from single-point freqs on the geometry used to calculate the reaction profile. this is simply because of errors in the freqs, which are used to calc the ZPE. there are special cases under which a reaction really can seem to have a negative activ. E, but I don't think that is the case with your work (see the CCL archives, or I can try to dig out the ref for you). See e.g. E. Lewars, Can. J. Chem., 2000, 78(2), 297-306. For estimating the T at which a compound becomes unstable, you could decide that a halflife of, say, 1 minute (or 1 hr) represents instability. You then have to estimate the T at which the rate const corresponds to that halflife. Rate constants can be calc ab initio from the Eyring equation, but this can be done accurately only for small molecules. See e.g. "The calc of thermodynamic quantities in Gaussian", by Joseph Ochterski, available from Gaussian Inc. ---------------------------------------------------------------- RESPONSE 3: (Dr. Sreedhara V Rao Chem Dept WA State Univ. Pullman, WA 99164) Thoughts on your question (1) Apparantly your reaction A=>B is highly exothermic and the barrier is quite low too. Tunneling in these kind of systems doesn't enhance the actual rate constant. If you calculate the vibrational imaginary frequency for the transition state it would be very small, which tells us the magnitude of tunneling-correction to the actual rate constant. Yes. You can consider the molecule A be stable (theoretical calculations should give all REAL vibrational frequencies), though it may be short lived. Since the reaction is highly exothermic, the variation in ZPV energies between the reactant and the transition state are barely minimal (TS structure resembles very close to reacant). Hence, the ZPVE corrections do not change the magnitude of activation barrier significantly. Also, state A should always have higher ZPVE than the ZPVE of the transition state (along the reaction coordinate, the breaking bond is partially broken at TS, while due to high exothermicity of the reaction, the forming bond is not really contributing to the total ZPVE of TS). The best example I can think of this kind of reaction is the 1:2-Hydrogen migration between acetylene to vinyledene H H C=C: ==> HC---C ==> HCCH H VINYLEDENE TS ACETYLENE Another similar reaction is the isomerization of HCN to HNC. Both the reactions are highly exothermic reaction (barrier existence is highly debated in acetylene/vinyledene isomerization) and vinyledene is short lived in picosecond timescales... HNC is observed experimentally. This should be quite true (i.e. trends in energies/rates etc.)even for other reactions involving different elements of the periodic table. Thoughts on your question (2). Depending on the rate constant scale (say, if you are satisfied that a rate constant of 10^12 at the room temperature is fast enough to consider that the reactant is stable/unstable). Some reactions reach the platau on the T-scale pretty fast depending upon the barrier (simple arrhenius plot). For example, in H- transfer reactions, the usual C-H frequency is about 3000cm-1 which turns out to be about 10^13sec-1 as the preexponential factor. If the activation barrier is exactly zero, then the rate constant is 10^13. Any positive barrier decreases the rate constant depending upon the temperature/amount of activation barrier. Hope my answers may not satisfy you completely, nevertheless they give you some insight. ---------------------------------------------------------------- RESPONSE 4: (Dr Kieran F Lim Biol. and Chemical Sciences (Lim Pak Kwan) Deakin University Geelong VIC 3217 AUSTRALIA) [for part (1)] - what level of "optimization" did you use? do you believe that your "A" is really a "reactant"? (what is A and B?) 0.2 kcal/mol is a very small energy. - the correct interpretation is *probably* a flexible molecule with vibrational and/or torsional freedom along the "reaction path" - tunnelling is only a reasonable interpretation if the reduced mass (as projected along the "reaction path") is sufficiently small and the "barrier" sufficiently thin [for part (2)] see any standard physical chemistry on the use of transition state theory to calculate rates of reaction. books like Benson, S. W. (1976). Thermochemical Kinetics. New York: Wiley. Benson, S. W. (1982). The Foundations of Chemical Kinetics. Malabar (FL): Krieger. Gilbert, R. G. and Smith, S. C. (1990). Theory of Unimolecular and Recombination Reactions. Oxford: Blackwells Scientific. discuss your problem in detail. they also give methods for estimating the pre-exponential Arrhenius A-factor. If you really have the changes in Gibbs free energy (as opposed to the electronic energy E, or the enthalpy H) delta G (TS) = delta H (TS) - temp delta S (TS) then you already have the exponential and pre-exponential Arrhenius = terms >from the temperature dependence of delta G (TS). again this is discussed in the above texts. ---------------------------------------------------------------- RESPONSE 5: (Pablo A. Denis) Hello david, last 19 of june I saw you mail in the ccl. I met with this problem several times and I don't have an official opinion. In the literature I didn't find an explanation of what's going on, you find = a minimum and a transition state, in energy everything is ok (the minimum = is bellow the ts but when you correct for zpe the transition state becomes more stable than the minimum (?) Can you summarize your answers or at least can you please send me the messages that the CCl suscribes had sent to you.