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Submerged Reaction Energy Barriers

The energy of your calculated transition state (TS) is lower than that of the reagents. That’s gotta be an error right? Well, maybe not.

Typically, in classical transition state theory, we associate the reaction barrier to the energy difference between the reaction complex and the TS, in other words, we associate the reaction barrier to the relative energy of the TS. However, this isn’t always the case, since the TS isn’t always located at the barrier, which simply may not exist or may be a submerged one, i.e. the TS relative energy is negative with respect to the reaction complex. This leads to negative activation energies, but one must bear in mind that the activation energy is not equal to the relative energy of the TS but rather to the slope of the Arrhenius plot, which in turn comes from the Arrhenius equation given below.

k = Aexp(Ea/RT) 
or in logarithmic form
Lnk = LnA + (Ea/RT)

The Arrhenius plot is then the plot of Lnk vs T-1, with slope Ea

Caution is advised since the apparent presence of such a barrier may be due to a computational artifact rather than to the real kinetics taking place, that’s why an IRC calculation must follow a TS optimization in order to verify the truthfulness of the TS; keep in mind that in classical transition state theory, we’re ‘slicing‘ a multidimensional map along a carefully chosen reaction coordinate but this choice might not entirely be the right one, or even an existing one for that matter. I also recommend to change the level of theory, reconsider the reaction complex structure (because a hidden intermediate or complex may be lurking between reactants and TS, see figure 1) and fully verifying the thermochemistry of all components involved before asserting that any given reaction under study has one of these atypical barriers.

NIST CCCBDB – Vibrational Scaling Factors & ThermoChem Data

The Computational Chemistry Comparison and Benchmark DataBase (CCCBDB) from the National Institute of Standards and Technology (NIST) collects experimental and calculated thermochemistry—related values for 1968 common molecules, constituting a vast source of benchmarks for various kinds of calculations.

In particular, scaling factors for vibrational frequencies are very useful when calculating vibrational spectra. These scaling factors are arranged by levels of theory ranging from HF to MP2, DFT, and multireference methods. These scaling factors are obtained by least squares regression between experimental and calculated frequencies for a set of molecules at a given level of theory.

Aside from vibrational spectroscopy, a large number of structural and energetic properties can be found and estimated for small molecules. A quick formation enthalpy can be calculated from experimental data and then compared to the reported theoretical values at a large number of levels of theory. Moments of inertia, enthalpies, entropies, charges, frontier orbital gaps, and even some odd values or even calculations gone awry are pointed out for you to know if you’re dealing with a particularly problematic system. The CCCB Database includes tutorials and input/output files for performing these kinds of calculations around thermochemistry, making it also a valuable learning resource.

Every computational chemist should be aware of this site, particularly when collaborating with experimentalists or when carrying calculations trying to replicate experimental data. The vastness of the site calls for a long dive to explore their possibilities and capabilities for more accurate calculations.

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