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As from the title, I want to do NEB-TS for chemical reactions in the liquid phase, and use the information to calculate reaction rates/kinetic rates.

I know that the NEB-TS is possible in the liquid phase using CPCM, for example. I'm not so clear on heterogeneous catalysis, for surface reactions. Logically, heterogeneous catalysis means I have components reacting, which adsorbs to the surface, and desorbs to form a product. Almost all microkinetic modelling I see mentions typically gas phase or solution phase, yet none of them mention the presence of a catalyst in the solution phase for the chemical reaction modelling. Do I have to physically model the surface in the quantum software?

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Usually if you have a heterogeneous catalyst, the best way to model it is to use a periodic slab (a thin plate that is periodic in two dimensions). A cluster model (i.e. approximating the catalyst as a nanoparticle) may also work. For heterogeneous catalysis in solution, the free space surrounding the catalyst can be described by e.g. CPCM, as usual.

I noticed that you have added the tag "orca" to your question. If you are specifically interested in studying surface catalysis with ORCA, then using a cluster model is the only choice. You may search for "CRYSTAL-QMMM" in the ORCA manual for details on how to perform such a calculation. Briefly, you take a suitably sized cluster from the surface of the catalyst (say ~100 atoms), and use this as the QM region. The catalyst atoms in immediate vicinity of the QM region are described by embedding potentials, and catalyst atoms further away are described by MM point charges. Then you can perform NEB-TS or essentially whatever calculation as usual. For example you can optimize the adsorbed structure by placing the adsorbent on the QM part of the surface (make sure that it does not get too near to any MM atom, otherwise the result may be inaccurate), and doing a geometry optimization where all MM atoms and the atoms described by embedding potentials are fixed.

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