# Reaction rate estimation for relatively complex reactions

I am looking for a summary of your favorite methods to estimate a reaction rate constant for a “complex” polyatomic reaction (requiring a cell of ~100 atoms) from ab initio methods (the one I have in mind currently is degradation of a surface layer of perovskite by superoxide, following $$\ce{4CH_3NH_3PbI_3^* + O_2^- \rightarrow 4PbI_2 + 2I2 + 2H_2O + 4CH_3NH_2}$$)

The most basic approach I know of would be to perform a DFT based NEB (nudged elastic band) calculation to identify the saddle point, compute the energy barrier $$E_a$$ in the ground state, and use a Boltzmann-like relationship $$\nu(T)=\nu_0.e^{-\beta E_a}$$ to speculate a characteristic reaction time at finite temperature. This approach has several weaknesses, in order of importance for me:

• For a “complex” reaction, finding the actual saddle point with a simple NEB seems like wishful thinking to me: there could be many reaction pathways, steps, etc… which makes it challenging to set up the NEB properly. The cost of testing many potential paths would also quickly become prohibitive  since a single NEB on a relatively large system is already pretty expensive (at least at my scale)
• The term $$\nu_0$$ is quite a big unknown. I’ve seen people use “educated guesses” to plug a reasonable value into it (like the frequency of oscillations in the crystal as an attempt frequency), but it seems quite hand-wavy and could easily be way off, which begs the question of knowing whether such a guess-based result has much significance

• It seems like a fairly harsh approximation to encapsulate all effects of thermalization in a Boltzmann law.

I have seen more sophisticated methods that build upon this and bring more accuracy, like the semiclassical transition state theory (SCTST), and basically alleviate the 2 last points, but still requires to find the saddle point, and leaves me with my issue #1, which is that it might be unpractical for more complex reactions (correct me if I'm wrong and if there are reliable methods to find this saddle point)

In summary:

What are the schemes available to compute reaction rates at finite temperatures for relatively big systems and multi-molecular reactions? I am particularly interested in accuracy vs complexity trade-off (i.e. I am interested in having a “not-so-precise-but-kinda-reasonable” result if it makes the calculations more affordable)

• Regarding this specific reaction, I'm afraid that no existing computational method may give a reliable estimate of the empirical reaction rate, given that the formed PbI2 will probably cover up the remaining perovskite. One can only hope to estimate the reaction rate in the first microsecond or so, where the surface of the perovskite can still be considered fresh Sep 24 at 8:37
• @wzkchem5 Yes, you are right, and this is what I am interested in (that's what I tried to mean by "surface reaction", i.e. only what happens to the first exposed layer) Sep 24 at 8:39
• I think ab-initio molecular dynamics could give you some useful information about the dynamics of the reaction, although I don't think a reliable reaction rate could be obtained for something complex as this. Sep 24 at 13:48