Dear Muhammad Fahad Arshad ,

A TS search requires an initial and final structure. For Cu2O and CuO, your final structure is well-defined but your initial structure is not. What would you start from? Vacuum? A Cu atom? An O atom or O2 molecule? Also, I'm not aware of any method that can be used to do variable-composition TS searches. It's an interesting idea but just that unfortunately.

Another option would be to do DFT molecular dynamics (MD) in the grand canonical ensemble (https://en.wikipedia.org/wiki/Grand_canonical_ensemble). However, there are two problems associated with this. First, like variable-composition TS searches, I'm not aware of any software package that offers this functionality. Second, DFT MD likely cannot access the relatively long timescales over which crystal growth takes place (i.e. μs to days). This is another interesting idea but computationally infeasible at the moment.

If you are clinging to DFT as your method of choice, you could try looking for/generating cluster expansion models for Cu2O or CuO (see equation 1 in this paper by my PI, https://iopscience.iop.org/article/10.1088/1361-651X/aa7e0c/pdf). Additionally, if you have a good intuition of the types of growth steps possible, you could calculate the barriers for those steps using DFT and perform kinetic Monte Carlo simulations (see this paper by my former PI for inspiration, https://www.sas.upenn.edu/rappegroup/research/Papers/Kim11p076102.pdf).

Now, if you aren't beholden to DFT, then you might be able to access the μs timescale using classical molecular dynamics (this is a GREAT code, https://lammps.sandia.gov). To access timescales longer than μs, you could also experiment with metadynamics (https://www.plumed.org, which can be used with a number of codes, including DFT ones).

As a final note, I recently published a method for automatically predicting surface phase diagrams using DFT-powered grand canonical Monte Carlo simulations (Article Automatic Prediction of Surface Phase Diagrams Using Ab Init...

I know this answer is long but I hope that it gives you some fresh ideas for achieving your goals. Best of luck and feel free to ask any follow-up questions that you may have.

Best,

Rob

Robert Wexler Thank you for your detailed answer

I learned a lot from your answer

I knew the limitations of DFT but Lammps combined with plumed might give some initial results

and I will look into Grand Canonical Ensemble